A machine can toss a golf ball a distance of 120 m on a level field when the machine is set to an angle of 30 degrees.How far can the machine toss a golf ball when it is set to an angle of 45 degrees?
A)85 m
B)98 m
C)140 m
D)150 m
E)170 m

Question

Quizplus · Accepted Answer

The range $R$ of a projectile launched with an initial velocity $v$ at an angle $\theta$ is given by the formula $R = \frac{v^2 \sin 2\theta}{g}$, where $g$ is the acceleration due to gravity. For angles of 30 degrees and 45 degrees, the ratio of their ranges is solely dependent on the $\sin 2\theta$ term because $v$ and $g$ remain constant. The sine of 60 degrees (since $2 \times 30 = 60$) is $\sqrt{3}/2$ and the sine of 90 degrees (since $2 \times 45 = 90$) is 1. Therefore, when the angle is increased from 30 degrees to 45 degrees, the range increases in proportion to the ratio of the sines of these angles. Since the range at 30 degrees is 120 m, and the sine ratio from 30 degrees to 45 degrees increases, the range at 45 degrees will be greater than 120 m. Among the given options, only 140 m is greater than 120 m and fits the expected increase in range.

A Machine Can Toss a Golf Ball a Distance of 120