7-23 away from her. The earth, in turn, pushes her away from it. Given: Carmen j

Question

7-23 away from her. The earth, in turn, pushes her away from it. Given: Carmen jumps upward with a force of 676 N. She is in contact with Carmen is skipping rope. When she jumps she pushes the earth the ground for 0.388 seconds, during which she lifts 15.5 cm before leaving the earth. Carmen has a mass of 57.0 kg. The earth has a mass of 5.98 × 1024 kg. Assume Carmen has a constant acceleration. (a) What is the unbalanced force acting on Carmer? (b) What is the impulse acting on Carmen just as she leaves the Find: earth? (c) What is the reaction force against the earth due to Carmen's jump? as she leaves? as a result of her jump? (d) What is the momentum of the earth due to Carmen's jump just (e) Whatis the velocity of the carth as i moves avasy fiom Carmen

Explanation / Answer

(A) F = m g = 57 x 9.81 = 559.2 N

(b) v^2 /2 = g h

v = sqrt(2 x 9.81 x 0.155) = 1.74 m/s

Impulse = change in momentum = 57 x (1.74 - 0 )

= 99.4 kg m/s

(c) F (t) = impulse

F = 99.4 / 0.388 = 256.2 N

(d) p = 99.4 kg m/s

(e) v= p / m = 99.4 / (5.98 x 10^24)

v = 1.66 x 10^-23 m/s

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