Relative Speed Calculation for Man Walking on a Moving Boat

[missashley]

Homework Statement

A ship cruises forward at Vs = 5 m/s relative to the Water. On deck, a man walks diagonally toward the bow such that his path forms an angle theta = 22 degrees with a line perpendicular to the boat's direction of motion. He walks at Vm = 2 m/s relative to the Boat.

Here is the image

http://img407.imageshack.us/img407/4973/boatum7.th.jpg

At what speed does he walk relative to the water? Answer in units of m/s.

Homework Equations

I'm unsure at what equations to use.

The Attempt at a Solution

Do I find the horizontal movement then minus that number to 5 m/s? Hmm.

Would I do cos 68 = adj/hypo. I got 68 because 90 - 22 = 68 and, I couldn't do cos 22 because it's not a right triangle when I draw in the "imaginary" lines. But what is adj and the hypo and the opposite lengths?

I'm at a lost. Help please

 

[learningphysics]

You need to add the velocity of the boat relative to water... to the velocity of the man relative to the boat...

take x to be the direction of the boat's motion..

take y perpendicular to x...

You know that the boat's velocity relative to water is:

vxboat = 5m/s
vyboat = 0m/s

Now, get the x and y components of the man's velocity relative to the boat:

what is vxman and vyman?

The hypoteneuse of your right triangle is 2m/s. The angle is 22 degrees. calculate the two legs of the right triangle.

 

[Architeuthis Dux]

I would approach this problem by first defining the variables and determining what information is given and what is needed. In this case, we are given the speed of the boat relative to the water (Vs = 5 m/s) and the speed of the man relative to the boat (Vm = 2 m/s). We are asked to find the speed of the man relative to the water.

To solve this problem, we can use vector addition. The man's velocity relative to the water (Vw) can be represented as the sum of his velocity relative to the boat (Vm) and the boat's velocity relative to the water (Vs).

Vw = Vm + Vs

Using trigonometry, we can break down the man's velocity relative to the boat (Vm) into its horizontal and vertical components.

Vm(horizontal) = Vm(cos22)
Vm(vertical) = Vm(sin22)

The horizontal component of the man's velocity will be in the same direction as the boat's velocity, so it will add to the boat's velocity. The vertical component will be perpendicular to the boat's velocity, so it will not contribute to the boat's speed.

Therefore, the man's velocity relative to the water can be calculated as:

Vw = Vm(horizontal) + Vs
Vw = Vm(cos22) + Vs

Plugging in the given values, we get:

Vw = (2 m/s)(cos22) + 5 m/s
Vw = 1.86 m/s + 5 m/s
Vw = 6.86 m/s

So the man's speed relative to the water is 6.86 m/s. This means that if an observer on the shore saw the boat and the man walking, they would see the man moving at a speed of 6.86 m/s in the same direction as the boat's motion.

In conclusion, by using vector addition and trigonometry, we can calculate the relative speed of a man walking on a moving boat.