Mike Powell In the 1991 World Track and Field Championships...

Mike Powell In the 1991 World Track and Field Championships in Tokyo, Mike Powell (Fig. 5-30) jumped $8.95 \mathrm{~m}$, breaking the 23 -year long-jump record set by Bob Beamon by a full $5 \mathrm{~cm}$. Assume that Powell's speed on takeoff was $9.5 \mathrm{~m} / \mathrm{s}$ (about equal to that of a sprinter) and that $g=9.80 \mathrm{~m} / \mathrm{s}^{2}$ in Tokyo. How much less was Powell's horizontal range than the maximum possible horizontal range (neglecting the effects of air) for a particle launched at the same speed of $9.5 \mathrm{~m} / \mathrm{s}$ ?

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Key Concepts

Optimal Launch Angle

The optimal launch angle for achieving maximum horizontal range in projectile motion is 45 degrees. At this angle, the combination of the vertical and horizontal components of the initial velocity is most effective for covering the longest distance, making it a key reference point when comparing actual projectile distances with theoretical maximums.

Projectile Motion

Projectile motion is the motion experienced by an object that is launched into the air and moves under the sole influence of gravity, with no propulsion after the initial launch. This requires analyzing the motion in horizontal and vertical components where the horizontal motion has constant velocity and the vertical motion is uniformly accelerated due to gravity.

Horizontal Range

The horizontal range of a projectile is the total distance it travels along the horizontal axis, from the point of launch to when it returns to the same vertical position. It is determined by the initial velocity, the launch angle, and the gravitational acceleration, and is typically calculated using the formula R = (v² sin(2?))/g.

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