The range of a projectile is directly proportional to the square of its velocity. If a motorcyclist can make a jump of 188.5 feet by coming off a ramp at 67 mph, find the distance the motorcyclist could expect to jump if the speed coming off the ramp were increased to 72 mph. Round to the nearest tenth of a foot.
A)220.4 feet
B)214.8 feet
C)213.4 feet
D)214.2 feet
E)217.7 feet

Question

Quizplus · Accepted Answer

The range $R$ of a projectile is directly proportional to the square of its velocity $v$, so we can write $R \propto v^2$. This means $R_1 / v_1^2 = R_2 / v_2^2$, where $R_1$ and $R_2$ are the ranges for velocities $v_1$ and $v_2$, respectively. Given $R_1 = 188.5$ feet at $v_1 = 67$ mph and $v_2 = 72$ mph, we find $R_2$ by solving $188.5 / 67^2 = R_2 / 72^2$. Solving for $R_2$ gives approximately 217.7 feet.

The Range of a Projectile Is Directly Proportional to the Square