A pebble rolls off the roof of Science Hall and falls vertically. Just before it

Question

A pebble rolls off the roof of Science Hall and falls vertically. Just before it reaches the ground, the pebble's speed is 21 m/s. Neglect air resistance and determine the height of Science Hall. A) 42 m B) 33 m C) 23 m D) 21 m E) 15 m A 51-kg woman runs up a flight of stairs in 5.0 s. Her net upward displacement is 5.0 m. Approximately, what average power did the woman exert while she was running? A) 5.0 kW B) 1.0 kW C) 0.75 kW D) 0.50 kW E) 0.25 kW What power is needed to lift a 49-kg person a vertical distance of 5.0 m in 20.0 s? A) 6.2 hp B) 0.16 W C) 0.03 W D) 120 hp The correct answer is not given

Explanation / Answer

33

Here the loss in Potential energy is converted into gain in Kinetic Energy

Thus

0.5*m*v^2 = mgh

Thus h = v^2/2g

            = (21)^2 / 2*9.8

            = 22.5 m = 23 m (option C)

34)

Power = W/t

          = mgh/t

         = 51*9.8*5/5

         = 499.8 W = 500 W = 0.5 kW (option D)

35)

m = mass = 49 kg

h = height gained = 5 m

t = time = 20 s

Power is given as

P = E/t = mgh/t

            = 49 x 9.8 x 5 / 20

            = 120.05 J/s = 120 hp = 0.16 W (option B)

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