Question

Rickey Henderson, baseball's record holder for stolen bases, approaches third base. He dives headfirst, hitting the ground at 7.68 m/s and reaching the base at 5.18 m/s, accelerating at -4.94 m/s/s. Determine the distance Rickey slides across the ground before touching the base.

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Answer 1

To determine the distance Rickey Henderson slides across the ground before touching the base, we can use the equation of motion:

v^2 = u^2 + 2as

where:

v = final velocity = 5.18 m/s

u = initial velocity = 7.68 m/s

a = acceleration = -4.94 m/s^2

s = distance

We want to find s, so let's rearrange the equation:

s = (v^2 - u^2) / (2a)

Now, let's substitute the given values:

s = (5.18^2 - 7.68^2) / (2 * -4.94)

Calculating this, we get:

s = (26.7884 - 59.2384) / (-9.88)

s = -32.45 / -9.88

s ≈ 3.28 meters

Therefore, Rickey Henderson slides approximately 3.28 meters across the ground before touching the base.

Step-by-step explanation:

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Answer 2

Answer: Approximately 0.65 meters

Step-by-step explanation:

Rickey Henderson, baseball's record holder for stolen bases, approaches third base. He dives headfirst, hitting the ground at 7.68 m/s and reaching the base at 5.18 m/s, accelerating at -4.94 m/s/s. We can use the kinematic equation v^2 = u^2 + 2as to determine the distance Rickey slides across the ground before touching the base, where v is the final velocity, u is the initial velocity, a is the acceleration and s is the distance.

Substituting the given values into the equation, we get:

(5.18 m/s)^2 = (7.68 m/s)^2 + 2 * (-4.94 m/s^2) * s

Solving for s, we find that Rickey slides a distance of approximately 0.65 meters across the ground before touching the base.