With what speed in miles/hr (1 m/s = 2.23 mi/hr) must an object be thrown to reach a height of 91.5 m (equivalent to one football field)?

Given:

a = -9.8 m/s2

vf = 0 m/s

d = 91.5 m

Find:

t = ??

vf2 = vi2 + 2*a*d

(0 m/s)2 = vi2 + 2*(-9.8 m/s2)*(91.5 m)

0 m2/s2 = vi2 - 1793 m2/s2

1793 m2/s2 = vi2

vi = 42.3 m/s

Now convert from m/s to mi/hr:

vi = 42.3 m/s * (2.23 mi/hr)/(1 m/s)

vi = 94.4 mi/hr

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