2 -140 points SerCP10 S.P 022 My Notes Ask Your Teacher 5.0-kg athlete leaps str

Question

2 -140 points SerCP10 S.P 022 My Notes Ask Your Teacher 5.0-kg athlete leaps straight up into the air from a trampoline with an ial speed of 8.0 m/s. The goal of this problem is to find the maximum ght she attains and her speed at half maximum height. (a) What are the interacting objects and how do they interact? TH This answer has not been graded yet (b) Select the height at which the athlete's speed is 8.0 m/s as -o What is her kinetic energy at this point? What is the gravitational potential energy associated with the athlete? (c) What is her kinetic energy at maximum height? What is the gravitational potential energy associated with the athlete? (d) Write a general equation for energy conservation in this case and solve for the maximum height. Substitute and obtain a numerical answer. (e) Write the general equation for energy conservation and solve for the velocity at half the maximum height. Substitute and obtain a numerical answer m/s

Explanation / Answer

athlete and tampoline

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b)

kinetic energy Ki = (1/2)*m*vi^2 = (1/2)*55*8^2 = 1760 J

gravitational potential energy Ui = m*g*yi = 0

c)

at maximum height velocity vf = 0

kinetic energy Kf = (1/2)*m*vf^2 = 0

maximum height yf = h

gravitational potential energy Uf = m*g*yf = m*g*h

(d)

conservation of energy : total mechanical energy remains at all points

Ui + Ki = Uf + Kf

1760 + 0 = 0 + 55*9.8*h

maximum height = 3.26 m

(e)

for yf = h/2

vf = ?

1760 + 0 = m*g*h/2 + (1/20*m*vf^2

1760 = (55*9.8*3.26) + 91/2)*55*vf^2

vf= 5.65 m/s <<<----ANSWER

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