Paleontologists estimate that if a Tyrannosaurus rex were totrip and fall, it wo

Question

Paleontologists estimate that if a Tyrannosaurus rex were totrip and fall, it would have experienced an upward normal force ofapproximately 264,000 N acting on itstorso when it hit the ground. Assume the torso has a mass of3860 kg. (a) Find the magnitude of the torso's upward acceleration asit comes to rest. (For comparison, humans lose consciousness withan acceleration of about 7g.)
(b) Assuming the torso is in free fall for a distance 1.59 m as it falls to the ground, how much time isrequired for the torso to come to rest once it contacts theground?
Paleontologists estimate that if a Tyrannosaurus rex were totrip and fall, it would have experienced an upward normal force ofapproximately 264,000 N acting on itstorso when it hit the ground. Assume the torso has a mass of3860 kg. (a) Find the magnitude of the torso's upward acceleration asit comes to rest. (For comparison, humans lose consciousness withan acceleration of about 7g.)
(b) Assuming the torso is in free fall for a distance 1.59 m as it falls to the ground, how much time isrequired for the torso to come to rest once it contacts theground?

Explanation / Answer

a) We know that F=ma, or a = F/m = (264000N)/(3860kg) = 68.4m/s2. This is approximately(68.4m/s2)/(9.8m/s2)g = 7.0g. b) We first have to find the speed at which it hits theground, which can be found by vf2 =vo2 + 2ax. vo = 0,because it starts at rest, a = 9.8m/s2, andx = 1.59m. Thus, vf = 5.58m/s. We thenuse the equation t = (vf - vo)/a for the timeat which it is on the ground to get that it would take (0 -(5.58m/s))/(-9.8m/s2) = 0.570s for it to come torest.

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