Question

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

Answer 1

Once u have the vertical motion model would the best way to solve for t be to use the quadratic formula??

Answer 2

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.

Answer 3

Yeah they both hit the water at the same time yet the book asks who hits it first.

Answer 4

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.

Answer 5

Wow jeez so Tyler enters the water 0.00002 of a second I didn't catch that because I just rounded it. Thanks Steve!!! :)