A spring-loaded dart gun is used to shoot a dart straight up into the air. The d

Question

A spring-loaded dart gun is used to shoot a dart straight up into the air. The dart reaches a maximum vertical height of 24 meters above its point of release. The same dart is shot up a second time from the same gun, but this time the spring is compressed only half as far (compared to the first shot). How far up (vertically) does the dart go this time? Neglect friction. Assume the spring is ideal and massless, and in each situation the dart ends up some vertical distance above the relaxed spring. 6.0 m 12 m 3.0 m 4.8 m E. 2.3 m

Explanation / Answer

from cosevration of energy

potetial energy in spring = potential energy in dart

(1/2)kx^2 = mg*24 ..(1)

x2 = x/2

(1/2)k(x^2)/4 = mg*h ..(2)

(1)/(2)

4 = 24/h

h = 6 m

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