A spring-loaded dart gun is used to shoot a dart straight up,and the dart reaches a maximum height of 24 meters.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 does the dart go this time (neglect all friction and assume the spring is ideal)?
A)6.0 m
B)12 m
C)3.0 m
D)48 m

Question

Quizplus · Accepted Answer

The maximum height reached by a projectile is proportional to the square of the initial velocity. If the spring is compressed only half as far, the initial velocity will be reduced by a factor of sqrt(2). Therefore, the maximum height will be reduced by a factor of (sqrt(2))^2 = 2. So, the dart will go up to a height of 24 m / 2 = 12 m.

A Spring-Loaded Dart Gun Is Used to Shoot a Dart