Question

Two children are playing a game in which they try to hit a small box on the floor with a marble fired from a spring loaded gun that is mounted on a table. The target box is horizontal distance D=2.20m from the edge of the table. Bobby compresses the spring 1.10 cm, but the center of the marble falls 27.0 cm short of the center of the box. How far should Rhonda compress the spring to score a direct hit? Assume that neither the spring nor the ball encounters friction in the gun.

Answer 1

Since the height of the table is constant, the time taken by the marble to reach the ground is same for all tries. Let

the time of flight be t.

For Bobby :

Horizontal distance traveled = 2.20 - 0.27 = 1.93 m

Time taken = t

Horizontal velocity = Distance / time = 1.93 / t

This velocity comes from the elastic potential energy of the spring.

Compression, x = 1.10 cm = 0.011 m

1/2*k*x^2 = 1/2*mv^2

k = m*(1.93 / t)^2 / (0.011)^2

For Rhonda :

Horizontal distance to be traveled = 2.20 m

Time taken = t

Horizontal velocity = Distance / time = 2.20 / t

1/2*kx^2 = 1/2*mv^2

Substitute for k and v to find x :

x = 1.25 cm