Finding the Time to Cross a River: Solving Vector Problems in Motion

[soicuw]

Homework Statement

A motorboat heads due east at 16 m/s across a river that flows due north at 9.0 m/s.
a. What is the resultant velocity (speed and direction) of the boat relative to the shore?
b. If the river is 136 m wide, how long does it take the motorboat to reach the other side?

Homework Equations

I'm not sure

The Attempt at a Solution

I tried to use the equation V_av=(delta)X/(delta)t and got 7.41 seconds, and the answer key says 8.5sec but I'm not sure how to get that answer.

 

[dav2008]

You must treat the velocity as a vector. Drawing a picture here helps. Setting the x-y coordinates to be across and along the river, respectively, you are given that the x-component of velocity is 16 m/s. Since the river is flowing north at 9 m/s you can say that it will carry the boat with the same speed so the y-component velocity of the boat is 9 m/s.

Now draw a picture. You can use simple geometric relationships to get what the problem is asking for.