Relative velocity and water skier

[dirk_mec1]

Homework Statement

Homework Equations

The Attempt at a Solution

The water skier makes an angle of 20 deg with the axis of the boat. I do not understand how to get the other angles.

 

[mfb]

Which angle do you want to find?

 

[J Hann]

Apparently, you need to assume that the skier is moving perpendicular to his tow line.
That is, his total velocity is perpendicular to the tow line even tho his linear velocity (parallel to the boat)
is at 50 deg.w.r.t. the tow line.

 

[J Hann]

I need to correct the above statement "his total velocity is perpendicular to the tow line".
A person riding in the boat would see the skier moving perpendicular the tow line.
That velocity then has to be added to the velocity of the boat to get the skier's total velocity.
Using geometry and the angles given you can construct the velocity triangle and solve with the Law of Sines.

 

[mfb]

I'm quite sure the person is moving along the length of the skier (relative to the water). (a) because that's how they work and (b) otherwise giving their direction would be pointless.

 

[J Hann]

I agree that skier is moving at 20 deg to the path of the boat.
Since he is at a fixed radius (10 m) from the boat his instantaneous path w.r.t an observer
on the boat must tangential w.r.t that radius.
That assumption agrees with the answer (a) of 80.8 m/s but it doesn't agree
with the answer for part (b)?

 

[haruspex]

but it doesn't agree with the answer for part (b)?

Did you forget to convert from kph to m/s?

 

[J Hann]

Did you forget to convert from kph to m/s?

Thanks. I agree with the given answer.