What is the velocity and angle of a man walking on a moving ship?

[anna_chem]

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 of 25 degrees with a line perpendicular to the boat's direction of motion. He walks at Vm= 3 m/s relative to the boat. What is his velocity relative to the water? And at what angle to his intended path does the man walk with respect to the water?

Homework Equations

vector magnitude and dot product

The Attempt at a Solution

I found the velocity of the man to be 7.8224 m/s by finding the x component of the velocity vector and the y component and then taking the magnitude. Our instructor told us we should use the dot product to find the angle that the man walks relative to the water, and I'm not sure if I calculated it right. I came up with 64.998 degrees.

 

[rl.bhat]

Velocity vector is written as
v = (vx*i + vy*j) vb = vb*i
So cosθ = v.vx/(v*vb)

 

[anna_chem]

So, our instructor helped us with the velocity magnitude. He gave [(5 + 3*cos25)^2 + (3*sin25)^2]^(1/2), is this not correct?

 

[rl.bhat]

So, our instructor helped us with the velocity magnitude. He gave [(5 + 3*cos25)^2 + (3*sin25)^2]^(1/2), is this not correct?

That is correct.
The formula in my post is to find the angle between the resultant velocity and the velocity of the boat with respect to the water.

 

[anna_chem]

Velocity vector is written as
v = (vx*i + vy*j) vb = vb*i
So cosθ = v.vx/(v*vb)

So, is it supposed to be cos(theta) = v*vx/(v*vb)? And is vb the velocity of the boat?

 

[rl.bhat]

So, is it supposed to be cos(theta) = v*vx/(v*vb)? And is vb the velocity of the boat?

Yes.

 

[anna_chem]

Thank you very much for your help!