resolving vectors

[kingjewel1]

I really dont know where to go with this one.

 

A boat sails across a straight river of uniform width W, starting from a point O on one bank of the river. The velocity of the river at a distance y from the bank is u(y)=ay(W-y), where a is a positive constant. The boat travels at a constant speed v relative to the current and steers a course set at a constant angle p between 0 and pi. in the downstream direction.

 

a) show that the velocity of the boat is

 

(u+vcosP)e1+(vsinP)e2.

 

b)at what time does the boat reach the other bank?

 

c) show that when the boat has reached the other bank, the downstream distance it has travelled is equatl to

 

[math]\frac{aW^3}{6vsinP}+WcotP[/math]

 

please help me

 

thanks in advance

[ed84c]

Well first draw it as a right angled triangle, and you should be able to see from it where the triganometery comes in. Then try using the suvat formulae.

[s pepperchin]

I don't know if you still need help with this but the first part is just vector addition, the second part is solving the y direction to go a distance W and the third part is multiplying the downstream velocty from part one by the time found in part two. If you need to see the actual proof let me know and I will post it.