A diver jumps off a 240 foot cliff. His forward motion is 20 feet per second. Th

Question

A diver jumps off a 240 foot cliff. His forward motion is 20 feet per second. The base of the cliff at the water edge extends 40 feet beyond the top edge of the cliff. Will the diver land in the water? Prove your answer. Draw a diagram of the problem. Safety engineers estimate that an elevator can hold 22 persons of 78 kg average mass. The elevator itself has a mass of 1150 pounds. The tensile stress tests show that the cable supporting the elevator can tolerate a maximum force of 30900 N. What is the greatest acceleration that the elevator's motor can produce without breaking the cable?

Explanation / Answer

inital velocity of diver is in horizontal direction,

hence initial vertical velocity component , uy = 0

y = 240 ft

a_y = g = 32.174 ft/s^2

Applying y = uy*t + ay* t^2 /2

240 = 0 + 32.174 t^2 /2

t = 3.86 sec

In horizontal,

x = ux * t = 20 ft/s * 3.86 s = 77.25 ft

which is greater than 40 ft.

hence diver will land in water.

3. Fmax - Mg = Ma_max

M = total mass = (22 x 78 kg) + (1150 x 0.454 kg) = 2238.1 kg

30900 - (2238.1 x 9.8) = (2238 x a)

a = 4 m/s^2

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