1. A 60 kg Olympic diver climbs up to a diving platform 8 meters above a swimmin

Question

1. A 60 kg Olympic diver climbs up to a diving platform 8 meters above a swimming pool.

(a) How much gravitational energy did she gain by climbing up to the platform (in Joules)?

(b) She then falls from the platform starting from rest. What is her kinetic energy when she enters the water (in Joules)?

(c) What is her velocity (meters/second) when she enters the water?

(d) What was her velocity (meters/second) half-way down in her fall?

(e) A 80 male diver then ascends the platform and falls to the water. What is the ratio of his kinetic energy entering the water compared to her kinetic energy?

(f) What the ratio of his velocity entering the water compared to her velocity?

Explanation / Answer

1. (A) delta(PE) = m g delta(h)

= (60)(9.8)(8)

= 4704 J

(B) PEi + KEi = PEf + KEf ( Energy conservation)

4704 + 0 = 0 + KE

KE = 4704 J

(C) Ke = m v^2 /2

4704 = 60 v^2 /2

v = 12.5 m/s

(D) (60 x 9.8 x 8) + 0 = (60 x 9.8 x 8 / 2) + 60 v^2 /2

v = 8.85 m/s

(E) ratio = m2 g h / m1 g h = 80/60 = 4/3 Or 1.333

(f) m g h = m v^2 /2 => v = sqrt(2 g h)

v is independent of mass.

so ratio = 1

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