An impala is an african antelope capable of a remarkable vertical leap

Question

An impala is an African antelope known for its remarkable vertical leap. In one recorded instance, a 45 kg impala crouched deeply, pushed straight up for 0.21 seconds, and reached a height of 2.5 meters above the ground. To achieve this leap, what force did the impala exert downward on the ground? Additionally, what is the ratio of this force to the impala's weight?

Mireya Berge · Accepted Answer

As the impala rises to its maximum height, its velocity will decrease to 0 m/s at the rate of 9.8 m/s each second. Let’s use the following equation to determine the impala’s after the force is exerted.

vf^2 = vi^2 + 2 a d, vf = 0, a = -9.8, d = 2.5

0 = vi^2 + 2 -9.8 2.5

vi^2 = 49

v = 7 m/s

The force must increase the impala’s velocity from 0 m/s to 7 m/s in 0.21 second

F = m * a

a = 7 ÷ 0.21 = 33⅓ m/s^2

F = 45 * 33⅓ = 1500 N

Let’s determine the impala’s weight.

Weight = 45 * 9.8 = 441 N

Ratio = 1500: 441

This is approximately 3.4 to 1.

Anonymous · Answer

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Ethan Friesen II · Answer

Impulse vector = Î = F̂ₐᵥₑΔt = Δmv̂ = mΔv̂ 
the deer's velocity in time Δt changes from 0 to vₒ. vₒ is the initial velocity for it's vertical jump
for vₒ we have 2.5 m = maximum height = vₒ²/[2g] 
=> vₒ = √[(2)2.5(9.81)] = 7 m/s (upwards)
Fₐᵥₑ(0.21) = mΔv = 45[7 - 0] = 315.16 
=> Fₐᵥₑ = 315.16 / .21 = 1500.77 N (downwards opp. the direction of vₒ)
Fₐᵥₑ / mg = 1500.77 / [45x9.81] ~= 3.4/1 
[please note: derivation of formula H = maximum height = vₒ²/[2g]
where vₒ is the initial vertical velocity. at the high point of a projectile the vertical velocity is = 0 as it reverses direction groundwards.
=> from v² = u² + 2as
=> 0² = vₒ² -2gH   or H = vₒ²/[2g] ]
hope this helps

Anonymous · Answer

Crouch Height

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An impala is an african antelope capable of a remarkable vertical leap

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