Asked by Taylor95

In a diving siblings showcase, 11yr old Hannah takes off from a 24.61 foot platform with an initial velocity of 9.7 ft/sec at the same time that her brother Tyler, who is older takes off from a 32.81 foot platform with an initial velocity of 4.51ft/sec. Who enters the water first? By how much? Round to the nearest hundredth. Please show all work thanks
Answered by Taylor95
Once u have the vertical motion model would the best way to solve for t be to use the quadratic formula??
Answered by Steve
Assuming the initial velocity is upward, the height of the divers is

H(t) = 24.61 + 9.7t - 16t^2
T(t) = 32.81 + 4.51t - 16t^2

Just solve each for t when the height is zero to see who takes longer. The quadratic formula would be the way to go.

I was mildly surprised at the answer.

Answered by Taylor95
Yeah they both hit the water at the same time yet the book asks who hits it first.
Answered by Steve
well, the answers are identical to a few decimal places. Just check the 3rd or 4th place to see which is actually a bit smaller.
Answered by Taylor95
Wow jeez so Tyler enters the water 0.00002 of a second I didn't catch that because I just rounded it. Thanks Steve!!! :)
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