Question

6. A swimmer bounces straight up from a diving board and falls feet first into a pool. She starts with a velocity of 4.00 m/s, and her takeoff point is 1.80 m above the pool. (3pt) a) How long are her feet in the air? b) What is her highest point above the board? c) What is her velocity when her feet hit the water?

Answer 1

The results of the calculation are;

a) The feet spends 0.41 s in air

b) The highest point above board is 2.62 m

c) The velocity when her feet hit the water is  7.2 m/s

What is the time spent in air?

From the data presented;

v = u + at

But v = 0 m/s at the maximum height thus;

0 = 4 - (9.8 * t)

4 = 9.8 * t

t = 4/9.8

t = 0.41 s

b) from;

h = ut - 1/2gt^2

h = (4 * 0.41) - (0.5 * 9.8 * (0.41)^2)

h = 1.64 - 0.82

h = 0.82 m

The total height above board = 0.82 m + 1.8 m = 2.62 m

c) The total time in air is obtained from;

h = ut + 1/2gt^2

u = 0m/s because she dropped off the board

h = 1/2gt^2

2.62 = 0.5  * 9.8 * t^2

t = √2.62/0.5  * 9.8

t = 0.73 seconds

Hence, the velocity when her feet hit the water is obtained from;

v = u + gt

when u = 0 m/s

v = gt

v = 9.8 *  0.73 s

v = 7.2 m/s

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