(3%) Problem 32: During an ice show, a 72.5-kg skater leaps into the air and is

Question

(3%) Problem 32: During an ice show, a 72.5-kg skater leaps into the air and is caught by an initially stationary 85 kg skater 50% Part (a) what is their final speed in meters per second, assuming negligible friction and that the 72.5 kg skater's initial horizontal speed is 3.85 m/s? Grade Summary Potential Submissions 0% 100% tan() | | ( | cosO cotan)asin)acosO atanO acotan)sinh(0 cosh0 tanh) cotanh0 Degrees Radians sinO Attempts remaining: 7 % per attempt) detailed view 123 0 END DEL CLEAR Submit Hint I give up! Hints: 0% deduction per hint. Hints remaining: 1 Feedback: 0%-deduction per feedback. 50% Part (b) How much kinetic energy is lost, in joules?

Explanation / Answer

Part (a)

Apply conservation of momentum -

mv1 = (m+M)*v2

=> 72.5*3.85 = (72.5+85)*v2

=> v2 = (72.5*3.85) / (72.5+85) = 1.77 m/s

So, final speed = 1.77 m/s

Part (b)

Initial Kinetic Energy, KEi = (1/2)mv1^2 = 0.5*72.5*3.85^2 = 537.32 J

Final Kinetic Energy, KEf = (1/2)(m+M)v2^2 = 0.5*157.5*1.77^2 = 246.72 J

So, loss in kinetic energy = KEi - KEf

= 537.32 - 246.72 = 290.6 J

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