Question

A long jumper can jump a distance of 8.0 m when he takes off at an angle of 45° with respect to the horizontal. Assuming he can jump with the same initial speed at all angles, how much distance does he lose by taking off at 30°?

a) 2.4 m
b) 3.2 m
c) 4.0 m
d) 4.8 m

Answer 1

To calculate the distance lost by taking off at 30° instead of 45°, one would need to compare the ranges at both angles. The range is calculated using the projectile's initial velocity, launch angle, and acceleration due to gravity.

Step-by-step explanation:

The question seeks to determine the distance lost by a long jumper who takes off at an angle of 30° instead of 45°, assuming the same initial speed. The projectile motion of the jumper can be analyzed using the equations for the range of a projectile, which considers the initial velocity, the angle of projection, and the acceleration due to gravity. To find the distance lost, one would calculate the range at both angles and then subtract the two.

For a projectile launched at an angle θ, the range R is given by the formula:
R = (v^2 * sin(2θ)) / g,
where v is the initial speed, g is the acceleration due to gravity, and θ is the launch angle. Given that the optimal range occurs at 45°, we can determine the range at 30° to find the difference.

Assuming the same initial speed, the comparison of ranges at 45° (optimal) and 30° will yield the distance lost.