A 35 g steel ball is held by a ceiling-mounted electromagnet 4.0 m above the floor. A compressed-air cannon sits on the floor, 4.4 m to one side of the point directly under the ball. When a button is pressed, the ball drops and, simultaneously, the cannon fires a 25 g plastic ball. The two balls collide 1.2 m above the floor. What was the launch speed of the plastic ball?

7.9 m/s

Explanation:

When both balls collide, they have spent the same time for their motions.

Motion of steel ball

This is purely under gravity. It is vertical.

Initial velocity, u = 0 m/s

Distance, s = 4.0 m - 1.2 m = 2.8 m

Acceleration, a = g

Using the equation of motion

Motion of plastic ball

This has two components: a vertical and a horizontal.

The vertical motion is under gravity.

Considering the vertical motion,

Initial velocity, u = ?

Distance, s = 1.2 m

Acceleration, a = -g                   (It is going up)

Using the equation of motion

Substituting the value of t from the previous equation,

Taking g = 9.8 m/s²,

This is the vertical component of the initial velocity

Considering the horizontal motion which is not accelerated,

horizontal component of the initial velocity is horizontal distance ÷ time.

The initial velocity is