Question

If Jason is playing football and Jason runs with the football west at a speed of 40.0 m/s and then turns and goes north at 5.0 m/s, what is the resultant velocity and 0?

Answer 1

The resultant velocity is 40.3 m/s at 7.1 degrees north of west

Explanation:

Jason's motion is divided into two parts.

At first, he moves west with a speed of

$v_x = 40.0 m/s$

Then, he moves north with a speed of

$v_y = 5.0 m/s$

The two velocities are at right angle, so they form the sides of a right triangle, and the magnitude of the resultant velocity can be calculated using Pythagorean's theorem:

$v=\sqrt{v_x^2+v_y^2}=\sqrt{40.0^2+5.0^2}=40.3 m/s$

And the direction can be found by using

$\theta = tan^{-1}(\frac{v_y}{v_x})=tan^{-1}(\frac{5.0}{40.0})=7.1^{\circ}$

So, 7.1 degrees north of west.

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