A boy of mass 62.6 kg is rescued from a hotel fire by leaping into a firefighter
ID: 1963272 • Letter: A
Question
A boy of mass 62.6 kg is rescued from a hotel fire by leaping into a firefighters' net. The window from which he leapt was 8.8 m above the net. The firefighters lower their arms as he lands in the net so that he is brought to a complete stop in a time of 0.40 s. Ignore air resistance.a.)What is his change in momentum during this time interval?
b.)What is the impulse on the net due to the boy during the interval? [Hint: Do not ignore gravity.]
c.) What is the average force on the net due to the boy during the interval?
Explanation / Answer
Mass of the boy m = 62.6 Kg velocity of boy just before hitting the net, u = Sqrt[2gh] = Sqrt[2 * 9.8 m/s^2 * 8.8 m] = 13.133 m/s Time of contact t = 0.4 s velocity of boy just after the collision, v = 0 (a) Change in momentum P = m(u - v) = (62.6 Kg)(13.133m/s - 0) = 822.13 Kg m/s (or) N s (b) Impulse = change in momentum = 822.13 Kg m/s (b) Average force F = P/t = ( 822.13 N s)/(0.4 s) = 2055.34 N
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