Relative Velocity Motorboat Problem

[rajumahtora]

Homework Statement

A motorboat is observed to travel 10 km/hr relative to Earth in the direction 37° north of east. If the velocity of the boat due to wind ONLY is 2 km/hr westward and that due to current is 4 km/hr southward, what is the magnitude and velocity of the motorboat due to its own power ?

2. Where I got stuck

I can't figure out if V of Boat with resp to Earth is given, what we have to find and whether "v due to wind..." means V of boat with respect to wind...if yes, what should i take as the velocity of Boat?

 

[phinds]

Well, it might help to first draw a vector of the boat's velocity relative to the Earth and see what that contributes to westward and southern velocities. What might you do after that?

 

[tiny-tim]

hi rajumahtora!

I can't figure out if V of Boat with resp to Earth is given, what we have to find and whether "v due to wind..." means V of boat with respect to wind...

i agree the wording is a little unsatisfactory

but the question is obviously about the addition and subtraction of velocities (as vectors), so just treat it as such

 

[haruspex]

I can't figure out if V of Boat with resp to Earth is given, what we have to find and whether "v due to wind..." means V of boat with respect to wind...if yes, what should i take as the velocity of Boat?

The question means that the boat's observed motion is a result of three things: wind, current and motor. You are told what the motion would be without current or motor, and what it would be without wind or motor. You are asked what it would be without wind or current.

 

[HalfLostAndSearching]

I would approach this problem by first clarifying the given information and what is being asked. It appears that we are given the velocity of the motorboat relative to Earth (10 km/hr at a direction of 37° north of east) and the velocities due to wind and current (2 km/hr westward and 4 km/hr southward, respectively). It is not explicitly stated, but I would assume that the velocity of the motorboat due to its own power is what is being asked for.

To solve for the magnitude and velocity of the motorboat due to its own power, we can use vector addition. We can break down the given velocity of the motorboat (10 km/hr at 37° north of east) into its x and y components. This would give us a velocity of 8 km/hr in the x-direction and 6 km/hr in the y-direction.

Next, we can add the velocity due to wind (2 km/hr westward) and the velocity due to current (4 km/hr southward) to the x and y components of the motorboat's velocity. This would give us a total velocity of 10 km/hr in the x-direction and 2 km/hr in the y-direction.

Finally, we can use the Pythagorean theorem to find the magnitude of the motorboat's velocity (10.2 km/hr) and the inverse tangent function to find the direction (11.3° north of east).

In conclusion, we can find the magnitude and velocity of the motorboat due to its own power by using vector addition and basic trigonometry. It is important to clarify the given information and what is being asked in order to solve the problem accurately.