How to Calculate the Correct Angle and Time to Cross a River in a Powerboat?

[mb8992]

A 370-m-wide river has a uniform flow speed of 1.7 m/s through a jungle and toward the east. An explorer wishes to leave a small clearing on the south bank and cross the river in a powerboat that moves at a constant speed of 5.6 m/s with respect to the water. There is a clearing on the north bank 93 m upstream from a point directly opposite the clearing on the south bank. (a) At what angle, measured relative to the direction of flow of the river, must the boat be pointed in order to travel in a straight line and land in the clearing on the north bank? (b) How long will the boat take to cross the river and land in the clearing?

would the equations to solve be:
t[5.6cos(theta) + 1.7] = 93
t[5.6sin(theta)] = 370

if not please help? if so how would i solve them?

 

[radou]

There is a neat graphical way of solving a). You just have to construct the equality $$\vec{v}_{B}=\vec{v}_{R}+\vec{v}_{B,R}$$. You know $$\vec{v}_{R}$$, you know the direction of $$\vec{v}_{B}$$, and you know the magnitude of $$\vec{v}_{B,R}$$. This is enough to construct the equation, and measure the angle.

 

[mb8992]

i don't understand

 

[DaveC426913]

Draw this out on paper - it will make more sense. I believe it is fairly simple vector addition.