I have a truck traveling forward at 20 m/s and I proceed to shoot a ball horizontally backwards from the back of the truck at 20 m/s. What direction does the ball go?

Refer to the diagram shown below.

Let the truck be traveling north at 20 m/s.

Let the ball be shot eastward at 20 m/s

The resultant velocity of the ball is

v = √ (20² + 20²) = 20√2 = 28.284 m/s

The direction is

θ = tan⁻¹ (20/20) = tan⁻¹ 1 = 45°

Answer:

The ball travels at 28.3 m/s at 45° relative to the direction of the truck.