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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 a accelerated movement due the gravity, according these equations:  

h = v0 * t + 1/2 * g * t^2  

v = v0 + g*t  

where h is height, v is final speed, v0 is initial speed, g is gravity constant equal to 9.8 m/s2 and t is time  

So the time to reach 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 the height of the slide is 2.5 meters

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