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# A child, starting from rest at the top of a playground slide, reaches a speed of 7.0 meters per second at the bottom of the slide. what is the vertical height of the slide? [neglect friction.]

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We know that the child will follow an accelerated motion due to gravity, according to these equations: h = v0 * t + 1/2 * g * t^2 v = v0 + g*t where h is the height, v is the final velocity, v0 is the initial velocity, g is the gravity constant equal to 9.8 m/s2 and t is the time So that the time to get to the bottom of the slide, v = v0 + g*t => 7 = 0 + 9.8*t t = 7/9.8 = 0.714 seconds, And then the height is: h = v0*t + 1/2*g*t^2 h = 0*0.714 + 1/2*9.8*0.714^2 = 2.5 meters So that the height of the slide is 2.5 metres