your motorboat can move at 30

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Relative Velocity and Riverboat Problems

• Vectors and Direction
• What is a Resultant?
• Vector Components
• Vector Resolution
• Component Addition
• Relative Velocity and River Boat Problems
• Independence of Perpendicular Components of Motion

Tailwinds, Headwinds, and Side Winds

To illustrate this principle, consider a plane flying amidst a tailwind . A tailwind is merely a wind that approaches the plane from behind, thus increasing its resulting velocity. If the plane is traveling at a velocity of 100 km/hr with respect to the air, and if the wind velocity is 25 km/hr, then what is the velocity of the plane relative to an observer on the ground below? The resultant velocity of the plane (that is, the result of the wind velocity contributing to the velocity due to the plane's motor) is the vector sum of the velocity of the plane and the velocity of the wind. This resultant velocity is quite easily determined if the wind approaches the plane directly from behind. As shown in the diagram below, the plane travels with a resulting velocity of 125 km/hr relative to the ground.

If the plane encounters a headwind, the resulting velocity will be less than 100 km/hr. Since a headwind is a wind that approaches the plane from the front, such a wind would decrease the plane's resulting velocity. Suppose a plane traveling with a velocity of 100 km/hr with respect to the air meets a headwind with a velocity of 25 km/hr. In this case, the resultant velocity would be 75 km/hr; this is the velocity of the plane relative to an observer on the ground. This is depicted in the diagram below.

Now consider a plane traveling with a velocity of 100 km/hr, South that encounters a side wind of 25 km/hr, West. Now what would the resulting velocity of the plane be? This question can be answered in the same manner as the previous questions. The resulting velocity of the plane is the vector sum of the two individual velocities. To determine the resultant velocity, the plane velocity (relative to the air) must be added to the wind velocity. This is the same procedure that was used above for the headwind and the tailwind situations; only now, the resultant is not as easily computed. Since the two vectors to be added - the southward plane velocity and the westward wind velocity - are at right angles to each other, the Pythagorean theorem can be used. This is illustrated in the diagram below.

In this situation of a side wind, the southward vector can be added to the westward vector using the usual methods of vector addition . The magnitude of the resultant velocity is determined using Pythagorean theorem. The algebraic steps are as follows:

10 000 km 2 /hr 2 + 625 km 2 /hr 2 = R 2

10 625 km 2 /hr 2 = R 2

SQRT(10 625 km 2 /hr 2 ) = R

103.1 km/hr = R

tan (theta) = (25/100)

theta = invtan (25/100)

theta = 14.0 degrees

If the resultant velocity of the plane makes a 14.0 degree angle with the southward direction (theta in the above diagram), then the direction of the resultant is 256 degrees. Like any vector, the resultant's direction is measured as a counterclockwise angle of rotation from due East.

Analysis of a Riverboat's Motion

The effect of the wind upon the plane is similar to the effect of the river current upon the motorboat. If a motorboat were to head straight across a river (that is, if the boat were to point its bow straight towards the other side), it would not reach the shore directly across from its starting point. The river current influences the motion of the boat and carries it downstream. The motorboat may be moving with a velocity of 4 m/s directly across the river, yet the resultant velocity of the boat will be greater than 4 m/s and at an angle in the downstream direction. While the speedometer of the boat may read 4 m/s, its speed with respect to an observer on the shore will be greater than 4 m/s.

The resultant velocity of the motorboat can be determined in the same manner as was done for the plane. The resultant velocity of the boat is the vector sum of the boat velocity and the river velocity. Since the boat heads straight across the river and since the current is always directed straight downstream, the two vectors are at right angles to each other. Thus, the Pythagorean theorem can be used to determine the resultant velocity. Suppose that the river was moving with a velocity of 3 m/s, North and the motorboat was moving with a velocity of 4 m/s, East. What would be the resultant velocity of the motorboat (i.e., the velocity relative to an observer on the shore)? The magnitude of the resultant can be found as follows:

16 m 2 /s 2 + 9 m 2 /s 2 = R 2

25 m 2 /s 2 = R 2

SQRT (25 m 2 /s 2 ) = R

5.0 m/s = R

tan (theta) = (3/4)

theta = invtan (3/4)

theta = 36.9 degrees

Given a boat velocity of 4 m/s, East and a river velocity of 3 m/s, North, the resultant velocity of the boat will be 5 m/s at 36.9 degrees.

Motorboat problems such as these are typically accompanied by three separate questions:

• What is the resultant velocity (both magnitude and direction) of the boat?
• If the width of the river is X meters wide, then how much time does it take the boat to travel shore to shore?
• What distance downstream does the boat reach the opposite shore?

The first of these three questions was answered above; the resultant velocity of the boat can be determined using the Pythagorean theorem (magnitude) and a trigonometric function (direction). The second and third of these questions can be answered using the average speed equation (and a lot of logic).

Consider the following example.

The solution to the first question has already been shown in the above discussion . The resultant velocity of the boat is 5 m/s at 36.9 degrees. We will start in on the second question.

The river is 80-meters wide. That is, the distance from shore to shore as measured straight across the river is 80 meters. The time to cross this 80-meter wide river can be determined by rearranging and substituting into the average speed equation.

The distance of 80 m can be substituted into the numerator. But what about the denominator? What value should be used for average speed? Should 3 m/s (the current velocity), 4 m/s (the boat velocity), or 5 m/s (the resultant velocity) be used as the average speed value for covering the 80 meters? With what average speed is the boat traversing the 80 meter wide river? Most students want to use the resultant velocity in the equation since that is the actual velocity of the boat with respect to the shore. Yet the value of 5 m/s is the speed at which the boat covers the diagonal dimension of the river. And the diagonal distance across the river is not known in this case. If one knew the distance C in the diagram below, then the average speed C could be used to calculate the time to reach the opposite shore. Similarly, if one knew the distance B in the diagram below, then the average speed B could be used to calculate the time to reach the opposite shore. And finally, if one knew the distance A in the diagram below, then the average speed A could be used to calculate the time to reach the opposite shore.

In our problem, the 80 m corresponds to the distance A, and so the average speed of 4 m/s (average speed in the direction straight across the river) should be substituted into the equation to determine the time.

It requires 20 s for the boat to travel across the river. During this 20 s of crossing the river, the boat also drifts downstream. Part c of the problem asks "What distance downstream does the boat reach the opposite shore?" The same equation must be used to calculate this downstream distance . And once more, the question arises, which one of the three average speed values must be used in the equation to calculate the distance downstream? The distance downstream corresponds to Distance B on the above diagram. The speed at which the boat covers this distance corresponds to Average Speed B on the diagram above (i.e., the speed at which the current moves - 3 m/s). And so the average speed of 3 m/s (average speed in the downstream direction) should be substituted into the equation to determine the distance.

distance = 60 m

The boat is carried 60 meters downstream during the 20 seconds it takes to cross the river.

The mathematics of the above problem is no more difficult than dividing or multiplying two numerical quantities by each other. The mathematics is easy! The difficulty of the problem is conceptual in nature; the difficulty lies in deciding which numbers to use in the equations. That decision emerges from one's conceptual understanding (or unfortunately, one's misunderstanding) of the complex motion that is occurring. The motion of the riverboat can be divided into two simultaneous parts - a motion in the direction straight across the river and a motion in the downstream direction. These two parts (or components) of the motion occur simultaneously for the same time duration (which was 20 seconds in the above problem). The decision as to which velocity value or distance value to use in the equation must be consistent with the diagram above . The boat's motor is what carries the boat across the river the Distance A ; and so any calculation involving the Distance A must involve the speed value labeled as Speed A (the boat speed relative to the water). Similarly, it is the current of the river that carries the boat downstream for the Distance B ; and so any calculation involving the Distance B must involve the speed value labeled as Speed B (the river speed). Together, these two parts (or components) add up to give the resulting motion of the boat. That is, the across-the-river component of displacement adds to the downstream displacement to equal the resulting displacement. And likewise, the boat velocity (across the river) adds to the river velocity (down the river) to equal the resulting velocity. And so any calculation of the Distance C or the Average Speed C ("Resultant Velocity") can be performed using the Pythagorean theorem.

Now to illustra te an important point, let's try a second example problem that is similar to the first example problem . Make an attempt to answer the three questions and then click the button to c heck your answer.

a. The resultant velocity can be found using the Pythagorean theorem. The resultant is the hypotenuse of a right triangle with sides of 4 m/s and 7 m/s. It is

Its direction can be determined using a trigonometric function.

b. The time to cross the river is t = d / v = (80 m) / (4 m/s) = 20 s

c. The distance traveled downstream is d = v • t = (7 m/s) • (20 s) = 140 m

An import ant concept emerges from the analysis of the two example problems above. In Example 1, the time to cross the 80-meter wide river (when moving 4 m/s) was 20 seconds. This was in the presence of a 3 m/s current velocity. In Example 2, the current velocity was much greater - 7 m/s - yet the time to cross the river remained unchanged. In fact, the current velocity itself has no effect upon the time required for a boat to cross the river. The river moves downstream parallel to the banks of the river. As such, there is no way that the current is capable of assisting a boat in crossing a river. While the increased current may affect the resultant velocity - making the boat travel with a greater speed with respect to an observer on the ground - it does not increase the speed in the direction across the river. The component of the resultant velocity that is increased is the component that is in a direction pointing down the river. It is often said that "perpendicular components of motion are independent of each other." As applied to riverboat problems, this would mean that an across-the-river variable would be independent of (i.e., not be affected by) a downstream variable. The time to cross the river is dependent upon the velocity at which the boat crosses the river. It is only the component of motion directed across the river (i.e., the boat velocity) that affects the time to travel the distance directly across the river (80 m in this case). The component of motion perpendicular to this direction - the current velocity - only affects the distance that the boat travels down the river. This concept of perpendicular components of motion will be investigated in more detail in the next part of Lesson 1 .

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Check your understanding.

1. A plane can travel with a speed of 80 mi/hr with respect to the air. Determine the resultant velocity of the plane (magnitude only) if it encounters a

a. 10 mi/hr headwind. b. 10 mi/hr tailwind. c. 10 mi/hr crosswind. d. 60 mi/hr crosswind.

a. A headwind would decrease the resultant velocity of the plane to 70 mi/hr .

b. A tailwind would increase the resultant velocity of the plane to 90 mi/hr .

c. A 10 mi/hr crosswind would increase the resultant velocity of the plane to 80.6 mi/hr .

This can be determined using the Pythagorean theorem: SQRT[ (80 mi/hr) 2 + (10 mi/hr) 2 ] )

d. A 60 mi/hr crosswind would increase the resultant velocity of the plane to 100 mi/hr .

This can be determined using the Pythagorean theorem: SQRT[ (80 mi/hr) 2 + (60 mi/hr) 2 ] )

2. A motorboat traveling 5 m/s, East encounters a current traveling 2.5 m/s, North.

a. What is the resultant velocity of the motor boat? b. If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore? c. What distance downstream does the boat reach the opposite shore?

a. The resultant velocity can be found using the Pythagorean theorem. The resultant is the hypotenuse of a right triangle with sides of 5 m/s and 2.5 m/s. It is

b. The time to cross the river is t = d / v = (80 m) / (5 m/s) = 16.0 s

c. The distance traveled downstream is d = v • t = (2.5 m/s)*(16.0 s) = 40 m

3. A motorboat traveling 5 m/s, East encounters a current traveling 2.5 m/s, South.

NOTE: the direction of the resultant velocity (like any vector) is expressed as the counterclockwise angle of rotation from due East.

c. The distance traveled downstream is d = v • t = (2.5 m/s) • (16.0 s) = 40 m

4. A motorboat traveling 6 m/s, East encounters a current traveling 3.8 m/s, South.

a. What is the resultant velocity of the motor boat? b. If the width of the river is 120 meters wide, then how much time does it take the boat to travel shore to shore? c. What distance downstream does the boat reach the opposite shore?

a. The resultant velocity can be found using the Pythagorean theorem. The resultant is the hypotenuse of a right triangle with sides of 6 m/s and 3.8 m/s. It is

NOTE: the direction of the resultant velocity (like any vector) is expressed as the counterclockwise direction of rotation from due East.

b. The time to cross the river is t = d / v = (120 m) / (6 m/s) = 20.0 s

c. The distance traveled downstream is d = v • t = (3.8 m/s) • (20.0 s) = 76 m

5. If the current velocity in question #4 were increased to 5 m/s, then

a. how much time would be required to cross the same 120-m wide river? b. what distance downstream would the boat travel during this time?

a. It would require the same amount of time as before ( 20 s ). Changing the current velocity does not affect the time required to cross the river since perpendicular components of motion are independent of each other.

b. The distance traveled downstream is

Note that an alteration in the current velocity would only affect the distance traveled downstream (and the resultant velocity).

• What is a Projectile?

A motorboat can move as fast as 30 km/h in still water. A man travels from one coastal town to another coastal town in 6 hours while going downstream. When he returns (upstream), he covers the same distance in 8 hours. What is the speed of the stream?

The correct option is b 30 7 km/h let the speed of the stream be x km/h. speed of motorboat = 30 km/h downstream speed = 30 + x km/h upstream speed = 30 − x km/h distance = speed x time. here, the diatance covered is the same. hence 6 ( 30 + x ) = 8 ( 30 − x ) ⇒ 180 + 6 x = 240 − 8 x ⇒ 6 x + 8 x = 240 − 180 ⇒ 14 x = 60 ⇒ x = 60 14 ⇒ x = 30 7 km/h hence, the speed of the stream is 30 7 km/h..

A motorboat goes downstream in river and covers a distance between two coastal towns in 6 hours. It covers this distance upstream in 8 hours. If the speed of the stream is 2 km/hr, find the speed of the boat in still water. [4 MARKS]

A motorboat travels 40 Km downstream in 4 hours and 30 Km upstream in 5 hours. Find the speed of the stream(in Km/hr).

The time taken to travel 30 km upstream and 44 km downstream is 14 hours. If the distance covered in upstream is doubled and distance covered in downstream is increased by 11 km then the total time taken is 11 hours more than earlier. Find the speed of the stream.

Do You Sail a Motor Boat?

August 30, 2022

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Owning a motorboat can be loads of fun. But, when it comes to using it, do you sail a motor boat or drive it? Let’s find out.

Most boat owners are always torn with the lingo when using a sailboat and a motorboat. These two are different, which is crucial to note.

You don’t sail a motorboat, but you drive it. When you turn on the engine to get it to move, you drive it. Driving the motorboat moves you through the water as you also engage the throttle. You start to drive the motorboat and direct it using a steering wheel towards your destination.

A motorboat is great since it gives you lots of freedom in the river, lake or ocean. But, it’s important to get some training before you drive off. The basic training helps you even know more about the pre-departure checklist.

Sailing a boat involves relying on wind force to push and steer the boat towards a direction or destination. A sailboat should have sails that trap wind and move the boat.

Table of contents

‍ do you sail a motor boat.

A motorboat or a powerboat can serve as a recreational vessel or for fishing. Since it has a motor that powers it, you drive the motorboat and not sail it. However, when you turn off the motor and start to steer it, you sail the motorboat.

When you own a motorboat, you get to drive it. A motorboat is different from a sailboat that you sail. Motorboats rely on the engine and fuel to move you from point A to B. Unlike a sailboat, these are fast vessels that achieve top speeds depending on the size and engine capacity.

If you plan to drive a motorboat, get some training and go through the pre-departure checklist before driving off.

Motorboats differ greatly from sailboats, but they also share some similarities. This is how you can pick them apart and know if you drive or sail them. For instance, sailboats tend to be calm and drift on the water.

The calm nature ensures you achieve maximum relaxation while on the waters. However, it’s all about the engine and driving it from one spot to another for a powerboat. Motorboats are not calm at all..

Usually, you won’t find a sail on a motorboat. It purely relies on the engine to drive from spot to spot. Whether you’re going fishing or just hanging out in the water, you can choose the speed. There is nothing quiet about a motorboat, given the engine's roar if you turn it on.

How Do Motor Boats Differ from Sail Boats?

You have to rely on the engine to move when you get a motorboat. It differs from a sailboat that relies on wind energy or rowing to get from point A to B.

Learning the difference between the two can help you choose the right one.

Motorboats are expensive. You can look into a sailboat if you want a cheaper option. Motorboats' whole design and structure make them costly.

It’s even possible for a motorboat to cost twice as much as a sailboat of the same size.

Sail Boats have the right of way

You must observe some rules in the open waters when you own a boat. Among the top rules is that sailboats have the right of way. This might come as a surprise to many, but owning a motorboat means you have to wait.

However, there is an exception to this rule regarding sailing and motorboats. If a motorboat has challenges maneuvering because of its size, it can have the right of way. It’s the best way to ensure the boat doesn’t run into problems that can cause it to capsize.

Large motor boats in open channels can seek the right of way when sailboats are around. It also applies in narrow channels and if the vessel has some mechanical issues. It needs to get to land fast hence can go before sailboats.

Motor Boats are Fast

Motorboats tend to move fast in open waters because of the engine's power that the boat uses. If it has a diesel engine, it can go even faster and get to destinations within no time. The factor of speed is why many people love to drive motorboats.

But, the speed also puts you at greater risk, especially when driving at the top speed of the motorboat. Top speeds can make a motorboat unstable and prone to capsizing. As for sailboats, they move at a slower pace and are more stable on the water.

Given how heavy sailboats can be, this reduces their average speed on the water. However, motorboats are lighter and can easily glide across the channels.

How to Drive a Boat

After noting that you drive and not sail a motorboat, you can now learn how it’s done. Driving a motorboat can be an exhilarating experience across the open waters. But, before you drive off, you need several lessons to master how it’s done.

You must learn some basics to drive a motorboat safely.

Pre-departure Checklist

Every motorboat requires checking before you take off. It’s where the pre-departure checklist comes in handy. When going through the list, check out the following.

• Life Jackets (at least one)
• Sound-producing Devices (boat horn, portable horn, and a whistle)
• Lights and Shapes
• Distress Signals (flares, day-shapes)
• Tools and Spares
• Fuel and Oil
• Fire Extinguishers

On top of these items, check the ventilation if the boat is enclosed and ensure the bilges are dry. Get to know the weather forecast before taking off and keep the radio on to get the latest forecast. Also, do some battery care and carry some spare batteries on board the motorboat.

After the checklist is complete, you can start the boat and take off.

Start the Boats

Most modern motorboats are simple to start. All you do is turn a key as you do in many vehicles. But, you have to note some safety features on the motorboat, such as the ‘kill switch.’ The engine safety cut-off appears as a small red knob next to the ignition.

The throttle is the next safety feature to observe before driving a motorboat. The throttle has to be neutral before you start the boat. It stops the boat from starting even with all other features on point until you move it.

The throttle releases the boat to start when you grasp it and pull back. Be aware of your surroundings since the boat will start to move as you do so.

Steer the Motor Boat

When the motorboat is in motion, you have to steer it, or you will move around aimlessly. Grasp the steering wheel, which resembles the one in cars.

When you turn the wheel, the motorboat will follow. But, this can be challenging if there are waves and lots of wind in the area.

Slowing a Motor Boat

Manipulating the throttle is one of the ways to get a boat to slow down. Motorboats don’t have brakes, unlike cars on the road. You have to learn how the boat operates and the stopping distance you need.

As you plan on stopping, ensure you are stable enough since boats don’t come with seat belts. Any sudden movement can topple you over, which you don’t want. Instead, be aware of your speed and how to slow down the boat safely.

With this information in mind, you can proceed to slow down your motorboat. Pull the throttle slowly back to neutral and pause for a moment. After that, shift it into reverse and apply some power. Pausing in neutral is crucial before going to reverse to avoid causing mechanical issues for the boat.

Most states need motorboat owners to take basic boating courses to learn how to drive motorboats. Doing so keeps you safe and everyone else driving or sailing in the same area. The training also takes you through steps like boat trimming and the different types of motorboats.

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About THE AUTHOR

Brian Samson

I have a deep love of houseboating and the life-changing experiences houseboating has brought into my life. I’ve been going to Lake Powell on our family’s houseboat for over 30 years and have made many great memories, first as a child and now as a parent. My family has a passion for helping others have similar fun, safe experiences on their houseboat.

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Can your baby drive a robot?

We are looking for babies between the ages of 6 to 18 months of age to test a prototype robotic mobility device that infants who do not have the ability to crawl or walk can use to move independently. To participate, babies should be able to sit independently or with moderate external support. They can be either developing typically or have delayed motor development.

Robot test sessions will take place on the campus of Ithaca College. Up to five robot sessions lasting approximately 20 minutes each will take place within not more than three weeks of time. We will also ask parents to complete a child history form and developmental questionnaire. Families will receive a $25 gift (or e-gift) card for each session their child attends.

Please also share this announcement with any families you think might be interested. Anyone who is interested in learning more about this research study, should contact:

Carole Dennis, ScD, OT  Professor Emerita, Occupational Therapy Ithaca College Phone (607) 351-1176 email [email protected]   IRB # 359