An object propelled from the ground with an initial velocity of 50 ft/s will reach a maximum height of 39.1 ft. If the initial velocity is increased 18%, by what percentage will the maximum height increase? Round percentages to the nearest integer.
A) 18%
B) 39%
C) 3%
D) 28%

Question

Quizplus · Accepted Answer

The maximum height $ h $ reached by an object propelled upwards with an initial velocity $ v $ in a gravitational field is given by the formula $ h = \frac{v^2}{2g} $, where $ g $ is the acceleration due to gravity. Increasing the initial velocity by 18% means the new velocity is $ 1.18v $. Substituting into the formula gives the new height as $ h_{new} = \frac{(1.18v)^2}{2g} = \frac{1.3924v^2}{2g} $. This is an increase of 39.24% in height, which rounds to 39%.

An Object Propelled from the Ground with an Initial Velocity