A catapult with a spring constant of 10,000 N/m is used to launch a target from the deck of a ship. The spring is compressed a distance of 0.5 m before the 1.56-kg target launched. What is the target's velocity as it leaves the spring?
Please help.
(A) 10m/s
(B) 20m/s
(C) 40m/s
(D) 30m/s

(C) 40m/s

Explanation:

Given;

spring constant of the catapult, k = 10,000 N/m

compression of the spring, x = 0.5 m

mass of the launched object, m = 1.56 kg

Apply the principle of conservation of energy;

Elastic potential energy of the catapult = kinetic energy of the target launched.

¹/₂kx² = ¹/₂mv²

where;

v is the target's  velocity as it leaves the catapult

kx² = mv²

v² = kx² / m

v² = (10000 x 0.5²) / (1.56)

v² = 1602.56

v = √1602.56

v = 40.03 m/s

v ≅ 40 m/s

Therefore, the target's velocity as it leaves the spring is 40 m/s