Two arrows are shot vertically upward. the second arrow is shot after the first one, but while the first is still on its way up. the initial speeds are such that both arrows reach their maximum heights at the same instant, although these heights are different. suppose that the initial speed of the first arrow is 31.8 m/s and that the second arrow is fired 1.82 s after the first. determine the initial speed of the second arrow.

These arrows will decrease their speed by the gravity according the following rule: Vf = Vi - g*t, where Vf is final speed, Vi initial speed, g is gravity constant and equal to 9.8 m/s2 and t is time elapsed. Then for the first arrow we can calculate the time to reach the màximum height, which is the point where final speed is equal to zero, so: 0=31.8 - 9.8*t => t=31.8/9.8=3.24 seconds Now we also know that both arrows reach maximum heights at same time, so for the second arrow we need to substrat the delay between both shots, the time till arrives at top position is in 3.24-1.82 = 1.42 seconds So then, inital speed of the second arrow is: 0=Vi-9.8*1.42 => Vi=13.96 m/s

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