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 take-off speed of 9.5 m/s? State your assumptions.

The maximum range obtainable by a person if he has a take-off speed of 9.5 m/s is 9.21 m

Explanation:

The only assumptions are that

Acceleration due to gravity = 9.8 m/s²

The equation for range of a projectile, R = (u² sin 2θ)/g

u = initial takeoff velocity = 9.5 m/s, θ = angle of jump.

To attain the maximum range, the (sin 2θ) has to be maximized to 1, that is,

Sin 2θ = 1 = sin 90°

2θ = 90°

θ = 45°

Therefore, the maximum angle of jump had to be 45°

R = (9.5² sin (2×45°))/9.8 = 9.5²/9.8 = 9.21 m