A powerboat heads northwest at 13 m/s relative to the water across a river that flows due north at 5.0 m//s. What is the velocity (both magnitude and direction) of the motorboat relative to the shore?

This problem involves the addition of two vectors: one is 13 m/s to the northwest (call this vector A) and the other is 5 m/s to the north (vector B). You add vectors by putting the tail of one against the head of the other, as in the attached figure, to get the resultant vector C.

To fnd the magnitude of C, use the law of cosines:


C^2 = A^2 + B^2 - 2AB cos(C)


Where C is the angle between A and B - you know this angle from the date you're given.
To fiind the direction of C, you can use the law of sines to find the angle B:


\frac B {sin(B)} = \frac C {sin(C)}

I got 16.9 m/s at 57.1 degrees north of west

I got 16.9 m/s at 57.1 degrees north of west

That's correct!

A 1.6 m tall girl throws a football at an angle of 41 degrees from the horizontal and at an initial velocity of 9.40 m/s. How far away from the girl will it land?

A 1.6 m tall girl throws a football at an angle of 41 degrees from the horizontal and at an inital velocity of 9.40 m/s. How far away from the girl will it land?

Please do NOT attach a new question onto an old thread. Please start a new thread instead.

But before you do - please take a shot at doing this homework problem yourself. If you need help by all means ask, but be sure to tell us how you've approached the problem and show us where you're getting stuck.

OK. I got 8.90 m