An athlete competing in the long jump leaves the ground with a speed of 9.14 m/s at an angle of 55° with the vertical.What is the length of the athlete's jump if air resistance is of no significance?
A)0.88 m
B)8.0 m
C)12 m
D)17 m
E)4.0 m

Question

Quizplus · Accepted Answer

The length of the athlete's jump can be calculated using the formula for the range of a projectile: $R = \frac{v^2 \sin 2\theta}{g}$, where $v$ is the initial velocity, $\theta$ is the angle of projection with the horizontal, and $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$). Given that the angle provided is with the vertical, we first convert it to the angle with the horizontal: $90° - 55° = 35°$. Substituting the given values: $R = \frac{(9.14)^2 \sin(2 \times 35°)}{9.8}$, we find that the length of the jump is approximately 8.0 meters.

An Athlete Competing in the Long Jump Leaves the Ground