Question

Chloe has a vertical velocity of 3 m/s when she leaves the 1m diving board

Chloe has a vertical velocity of 3m/s she leaves the 1m diving board. At this instants, her center of gravity is 2.5m high.

a) How high will Chloe go?

b) How long will Chloe be in the air before she touches the water? Assume that her hands enter the water when her center of gravity is 1m high.

02 = 32 + 2 (-9.8)d;

0 = 9 + (-19.6)*d; -9 =

(-19.6)d; d = 0.46 m.

Chloe will travel 0.46 meters upward due to the takeoff velocity of 3 m/s. Or Chloe's center of gravity will be 2.96 m (2.5 + 0.46) above the water level.

b. Chloe's time in the sir includes time to travel upward and time to travel downward until his hands touches the water. The time travel upward depends on the takeoff velocity and the gravity ( ). ; 0 = 3 + (-9.8)t; -3 = (-9.8)t; t = 0.31 seconds. The time travel downward depends on the gravity and displacement. The total vertical displacement will be 0.46 m plus 1.5 m this is due to his final position where his center gravity is 1 meter above the water. Therefore, the displacement from the end of the previous downward travel is 2.5-1 = 1.5 m. So the total downward displacement is 1.96 meters. ; -1.96 = 0 t + 0.5 (-9.8)t2; -1.96 = (-4.9) t2; t2 = 0.4; t = 0.63 seconds which is the time for traveling downward. The total time in the air will be 0.31 + 0.63 = 0.94 seconds.

calculation may be wrong but concept is right.

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