spiderman steps off the top of a tall building. He falls freely to the ground a

Question

spiderman steps off the top of a tall building. He falls freely to the ground a distance h. He falls a distance h/5 in the last t seconds of his fall. What is the height h of the building in terms of t?

Explanation / Answer

let T be the total time needed to reach the ground, so : v = u + g (T - t) => v = g(T - t) , where v is the velocity at h/5 height. and : h = 0 + 1/2 g T^2 => h = 1/2 g T^2 => T = sqrt (2h/g) another eqn can be made: h/5 = vt + 1/2 g t^2 => h/5 = g(T - t) t + 1/2 g t^2 => h/5 = g(sqrt (2h/g) - t) t + 1/2 g t^2 => h = 5g (sqrt (2h/g)t - t^2 + t^2 /2 ) => h = 5g (sqrt (2h/g)t - t^2 / 2)

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