# Physics - Relative Motion Homework Help

• L_0611
In summary: So the boat will not be quite pointed north. In summary, the ferryboat's velocity is affected by the river's current, and without compensation, it would have a new velocity of 5.00m/s at an angle of 41° east of north. The boat's velocity across the river is 4.00m/s, and it would take 32 seconds to travel across the 128m wide river. With compensation, the boat would be headed at a 54° angle and would travel straight across the river to the north.
L_0611

## Homework Statement

A ferryboat, whose speed in still water is 4.00m/s, must cross a river whose current is 3.00m/s. The river runs from west to east and is 128m wide. The boat is pointed north.

a) If the boat does not compensate for the flow of the river water and allows itself to be pushed off course, what would be the new velocity of the boat? State both the magnitude and the direction of the velocity of the boat relative to the riverbank.

b) In part (a), what is the velocity of the boat across the river? How long would it take the boat to travel across the river?

c) The boat now compensates for the river current so that it travels straight across the river to the north without being pushed off course.

## Homework Equations

let Vbw represent velocity of boat relative to the water.
let Vbs represent velocity of the boat relative to the shore.
let Vws represent velocity of the water relative to the shore.
Vbs=Vbw+Vws

pythagorean theorem using the variables Vbs²=Vbw²+Vws²

V=d/t (not sure how to write the vector symbols for velocity and distance, but I know they're supposed to be there and that is what V and d mean)

## The Attempt at a Solution

a) Vbs²=Vbw²+Vws²
Vbs²= (4.00m/s)²+(3.00m/s)²
Vbs²=16.00m/s+9.00m/s
Vbs²=25.00m/s
Vbs=*√25.00m/s
Vbs= 5.00m/s {41º E of N}

Θ = tan-¹ (3.00m/s / 4.00m/s)
= 41º
∴ If the boat does not compensate for the flow of the river water and allows itself to be pushed off course, the new velocity of the boat would be 5.00m/s {41º E of N}

b)
In part (a) the velocity of the boat across the river is 4.00m/s

V=d/t
t=d/V
t= 128m/4.00m/s
t= 32s

∴ it would take the boat 32s to travel across the river.

c) Vbs=Vbw+Vws
Vbs=4.00m/s {at some angle} + 3.00m/s {E}

to find the angle use inverse Sine function.

θ= Sine-¹(3.00m/s / 4.00m/s)
θ= 54°

∴ If the boat now compensates for the river current so that it travels straight across the river to the north without being pushed off course, it should be headed at 54° angle.

Please correct any of my work if I have made any mistakes at any point in solving this problem. Thanks for your help.

Your methods are all correct, but in each case the angle seems a bit too large. atan(0.75) = 36.9 degrees and asin(.75) = 48.6 degrees. That last must be about right because sin(45 deg) = sqrt(1/2) = .707...

## What is relative motion in physics?

Relative motion in physics is the motion of an object with respect to another object. This means that the movement of an object is described in relation to the movement of another object, rather than in absolute terms.

## How is relative motion different from absolute motion?

Absolute motion refers to the movement of an object with respect to a fixed reference point, such as the ground or a stationary object. Relative motion, on the other hand, takes into account the movement of both objects and describes their motion in relation to each other.

## What is the formula for calculating relative velocity?

The formula for relative velocity is vrel = vA - vB, where vrel is the relative velocity, vA is the velocity of one object, and vB is the velocity of another object.

## What is the difference between relative velocity and relative speed?

Relative velocity refers to the speed and direction of an object with respect to another object, while relative speed only refers to the numerical value of the difference in speeds between two objects, regardless of direction.

## How is relative motion used in real-life scenarios?

Relative motion is used in many real-life scenarios, such as calculating the velocity and trajectory of objects in motion, understanding the motion of celestial bodies in relation to each other, and designing transportation systems that account for the movement of multiple objects.

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