Question

The world long jump record is$\mathbf{8}\mathbf{.}\mathbf{95}$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$\mathbf{9}\mathbf{.}\mathbf{5}$m/s? State your assumptions

Short answer

The maximum range is obtained by the person .$R_{max}=9.21m$

Step-by-step solution

Definition of final velocity 

When gravity first exerts a force on an item, its initial velocity indicates how fast it travels. The final velocity, on the other hand, is a vector number that measures a moving body's speed and direction after it has reached its maximum acceleration.

Given data:

• Initial take-off speed, v_i =$9.5$ m/s.
• To achieve maximum range (R_max), the angle θ should be$45°$ for a projectile.

Finding value of maximum range obtained by person

The equation for the range for a projectile is given by

$R=\frac{{V_i}^2\sin \left(2{\theta }_i\right)}{g}$……………….(1)

Substituting the given values in equation 1, we get

$$\begin{gathered} R_{max}=\frac{{(9.5)}^2\times \sin (2\times 45°)}{9.8} \\ =\frac{{(9.5)}^2\times \sin (2\times 45°)}{9.8} \\ =\frac{90.25\times \sin 90°}{9.8} \\ =9.21m \end{gathered}$$

The maximum horizontal distance covered by the person, .$R_{max}=9.21m$

Assumptions

Mike Powell's long jump record is$8.95$ m, so he must have taken off with a velocity nearly equal to$9.5$m/s, and θshould have been nearly equal to .$45°$