Question

A small spring-loaded launcher is designed to fire steel ball bearings with masses of 0.3 kg . When setting the launcher, you compress the spring a distance of 14 cm . You then fire the launcher straight up and find that the projectiles reach a maximum height of 0.9 m above the point that they leave the launcher. You load another ball bearing, compress the spring a distance of 20 cm , and place it horizontally at the edge of a table that is 0.5 m tall.

You fire the ball from the edge of the table. How far from the base of the table does it hit the ground?

Answer 1

Given values:

Mass of the steel ball, m = 0.3 kg

Compression in the spring, x = 14 cm = 0.14 m

H_max. = 0.9 m

Height of the table, h = 0.5 m

x’ = 0.20 m

From the conservation of energy:

The potential energy stored in spring due to compression = potential energy gained by the ball at the maximum height

Let the initial speed of another ball be v

Again from the conservation of energy:

Let the time taken by the ball to reach the ground be t

From the kinematics equation:

Distance from the base of the table:

R = vt = 0.66 x 0.0367 = 0.0242 m