Dave, who has a mass of 94kg, stands motionless on a force plate then initiates

Question

Dave, who has a mass of 94kg, stands motionless on a force plate then initiates a counter-movement vertical jump. At the instant he starts the counter movement, his vertical ground reaction force decreases to 306N and remains constant for 0.15s. His vertical ground reaction force then increases to 1997N and remains constant for 0.17s at which time he left the ground. What was his vertical velocity at the instant he left the ground? Answer is 0.961, not sure how you get there if you could show me step by step

Explanation / Answer

weight of Dave = 94*9.8 = 921.2 N

impulse of initial reaction = 306*0.15 = 45.9 N-s

impulse of second reaction = 1997*0.17 = 339.49 N-s

Total upward impulse = 339.49+45.9 = 385.39 N-s

down force, i.e, Dave's weight remains constant through out = 921.2(0.15+0.17) = 294.784 N-s

Net upward impulse = 385.39-294.784 = 90.06 N-s

net upward umpulse is equaal to the net upward momentum p = mv

initial vertical velocity v = 90.606/94 = 0.964 m/s

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