Runs down a slide

Classical Mechanics Level 2

A boy runs down a slide height 4.0 m 4.0\text{ m} from home. Considering g = 10 m/s 2 g = 10\text{ m/s}^2 and 20% of the mechanical energy is dissipated during the trip, determine the speed at which the child hits the ground.


The answer is 8.

Lucas Sousa by Lucas Sousa , 26, Brazil

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1 solution

Tom Engelsman
Sep 15, 2019

The required energy balance equation is just:

P E = K E + E f r i c t i o n ⇒ m g h = 1 2 m v 2 + 0.2 m g h ⇒ 0.8 m g h = 1 2 m v 2 ⇒ 1.6 g h = v PE = KE + E_{friction} \Rightarrow mgh = \frac{1}{2}mv^2 + 0.2 mgh \Rightarrow 0.8mgh = \frac{1}{2}mv^2 \Rightarrow \sqrt{1.6gh} = v .

This ultimately computes to:

v = 1.6 ( 10 ) ( 4 ) = 64 = 8 v = \sqrt{1.6(10)(4)} = \sqrt{64} = \boxed{8} m/s.

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