Question

In the 1991 World Track and Field Championships in Tokyo, Mike Powell jumped 8.95m, breaking by a full 5cm the 23-year long-jump record set by Bob Beamon. Assume that Powell’s speed on takeoff was 9.5 m/s (about equal to that of a sprinter) and that g=9.80$\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$in Tokyo. How much less was Powell’s range than the maximum possible range for a particle launched at the same speed?

Short answer

Powell’s range was 0.259m less than the maximum possible range for a particle launched at the same speed

Step-by-step solution

Given information

Powell’s jump is 8.95m

Powell’s speed at the time of takeoff is $v_0=9.50\mathrm{m}/\mathrm{s}$

Powell’s gravitational acceleration$g=9.8\mathrm{m}/{\mathrm{s}}^2$

To understand the concept

This problem deals with the horizontal range of the particle which is nothing but the horizontal distance from the launch point at which the particle returns to the launch height. Using the formula for the range of the particle, the maximum range of the particle can be found. It is possible to determine how much less was Powell’s range than the maximum possible range for a particle, when they are launched at the same speed.

Formula:

The particle’s horizontal range can be given as,

$R=\frac{v_0^2}{g}\sin 2∆$ (i)

Where $v_0$ is the initial velocity of the particle.

$R=R_{max}when∆=45°$

To find the maximum possible range for a particle

Using equation (i), the maximum range will be,

$$\begin{gathered} R_{\max }=\frac{9.50\mathrm{m}/\mathrm{s}}{9.8\mathrm{m}/{\mathrm{s}}^2}\sin \left(90°\right) \\ {R}_{max}=9.209\mathrm{m} \end{gathered}$$

To find the difference between Powell’s jump and Rmax

It is given that,

$$\begin{gathered} ∆R=R_{max}-8.95\mathrm{m} \\ ∆\mathrm{R}=0.259\mathrm{m} \end{gathered}$$

Therefore, Powell’s range was 0.259 m was less than the maximum possible range for a particle launched at the same speed.