Question

The world long jump record is 8.95 m (Mike Powell, USA, 1991). Treated as a projectile, what is the maximum range obtainable by a person if he has a takeoff speed of 9.5 m/s? State your assumptions.

The maximum range obtainable by the person is approximately:
a) 8.0 m
b) 9.0 m
c) 10.0 m
d) 11.0 m

Answer 1

The maximum range obtainable by a person with a take-off speed of 9.5 m/s is approximately 8.09 m.

Step-by-step explanation:

To determine the maximum range obtainable by a person treated as a projectile with a take-off speed of 9.5 m/s, we can use the formula for the range of a projectile. Assuming that air resistance is negligible and the initial height is zero, the maximum range can be calculated using the formula:

Range = ((Initial Velocity)² * sin(2θ)) / g

where θ is the launch angle and g is the acceleration due to gravity. In this case, we can assume the launch angle is 45 degrees to maximize the range.

Plugging in the given values:

Range = (9.52 * sin(2 * 45)) / 9.8

Simplifying the equation, we get:

Range ≈ 8.09 m