BIO Force During a Jump.? When jumping straight up from a crouched position, an average person can reach a maximum height of about 60 cm. During the jump, the person’s body from the knees up typically rises a distance of around 50 cm. To keep the calculations simple and yet get a reasonable result, assume that the ?entire body? rises this much during the jump. (a) With what initial speed does the person leave the ground to reach a height of 60 cm? (b) Draw a free-body diagram of the person during the jump. (c) In terms of this jumper’s weight w, what force does the ground exert on him or her during the jump?
Solution 21E Step 1: Height reached by the person (h) = 60cm or 0.6m Problem (a) Step 1: To find Initial speed required to reach the height 2 2 v = v 0 + 2aS ----- (1) Here S = h 2 a = -9.8 m/s (jumping upward) v = 0 m/s (final velocity = 0 when maximum height) Step 2: Substituting known values and rearranging (1) v = 2gh 0 v0 = 2 9*8 0.* v0 = 3.43 m/s Problem (b) Free-body diagram Problem (c) Step 1: To find the force exerted on the man F = mg + ma ----- (2) During the jump, the person’s body from the knees rises a distance of around 50 cm. Therefore x = 0.5m. Step 2: To find acceleration produced 2 2 v = v 0 2ax 2 v = 0 2 v 0 = 2ax