College Physics by Openstax, Problem 2.35

Consider a grey squirrel falling out of a tree to the ground.

(a) If we ignore air resistance in this case (only for the sake of this problem), determine a squirrel’s velocity just before hitting the ground, assuming it fell from a height of 3.0 m.

(b) If the squirrel stops in a distance of 2.0 cm through bending its limbs, compare its deceleration with that of the airman in the previous problem.

SOLUTION:

Part a

We are given 

v_0=0\:m/s

a=-9.8\:m/s^2

x=-3.0\:m

Note that the acceleration is due to gravity and its value is constant at a=-9.8\:m/s^2. Also, the distance, x, is negative because of the direction of motion. For free fall, downward motion is considered negative. To solve for the velocity just before it hits the ground, we have

v^2=v_0^2+2ax

v^2=\left(0\:m/s\right)^2+2\left(-9.8\:m/s^2\right)\left(-3.0\:m\right)

v=\sqrt{2\left(-9.8\:m/s^2\right)\left(-3.0\:m\right)}

v=7.7\:m/s

Part b

We are given

v=0\:m/s

v_0=7.7\:m/s

x=0.02\:m

To solve for the acceleration, we have

a=\frac{v^2-v_0^2}{2x}

a=\frac{\left(0\:m/s\right)^2-\left(7.7\:m/s\right)^2}{2\left(0.05\:m\right)}

a=-1.5\times 10^3\:m/s^2

This is approximately 3 times the deceleration of the pilots from the previous problem, who were falling from thousands of meters high.

 

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