8. Consider the Olympic sport of diving. The more time the athlete spends in the

Question

8. Consider the Olympic sport of diving. The more time the athlete spends in the air, the greater the potential to complete difficult maneuvers. Off of a 3 m spring board with a stiffness of 5920 N/m, a diver with a mass of 52 kg will maximally deflect the board 0.5 m from its equilibrium position. Assume that all of the strain energy stored in the board is returned to the diver in the vertical direction.

a. How much time will the diver be in the air when using the 3 m spring board? (1)

b. What will the diver’s velocity be when they hit the water? (1)

c. How much time will a diver spend in the air when diving off of a 10 m platform with an initial velocity of 0 m/s in the vertical direction? (1)

d. What will the diver’s velocity be when they hit the water? (1)

Explanation / Answer

So since the spring board can bend and store energy, Pot energy stored in board will be converted into Kinetic energy of swimmer

1/2 mv2 = 1/2 k x2

52 * v2 = 5920 * 0.52

'v = 5.33 m/s in vertical direction

so since the board is at 3m height from water level ,

first swimmer will go upwards, v = u - 10t

t = 1.876 sec

so same time to come down, t = 1.876 * 2 = 3.75 sec

now it has got inital velocity 5.33 in downward direction

and has to cover 3 m now to reach water

so , S = ut + 1/2 at2

t = 0.41 sec

a) so total time = 4.16 sec

b) v = u + 10 * 0.41

= 9.43 m/s

c) so height to cover= 10 m

so S= ut + 1/2 at2

10 = 5 t2

so t = 1.414 sec

d) v = u + 10 * 1.41

= 14.1 m/s

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