Newtons Laws of Motion Question

[laurenflakes]

Homework Statement

Paleontologists estimate that if a Tyrannosaurus rex were to trip and fall, it would have experienced a net force of approximately 256,700 N acting on its torso when it hit the ground. Assume the torso has a mass of 3710 kg.

(a) Find the magnitude of the torso's upward acceleration as it comes to rest. (For comparison, humans lose consciousness with an acceleration of about 7g.)

(b) Assuming the torso is in free fall for a distance 1.39 m as it falls to the ground, how much time is required for the torso to come to rest once it contacts the ground?

Homework Equations

F = (m)(a)

The Attempt at a Solution

Immediately it appeared to me that by using the equation that states that the sum of the net forces is equal to the mass of the object in kilograms multiplied by the acceleration of the object. I rearranged the equation to solve for acceleration as such:

256700 N / 3710 kg = 69.19 m/s^2

However, this answer is incorrect.. I don't see what I am doing wrong? Help??!? :(

 

[laurenflakes]

Nevermind! I got the answer :)

What I was doing wrong was not taking into account the affect of the weight on the Net force.

By determining the weight of the T-Rex in Newtons (3710)(9.8) = 36358 and subtracting this number from the original net force 256700 - 36358 = 220342 N then taking that number and dividing by the mass 220342 N/3710 kg I was able to get the correct acceleration which was 59.39 m/s^2 :)

Still stumped on part b though. Now that I know the acceleration I tried using the equation v(final) ^2 = v(initial)^2 + 2(a)(d). With my final velocity being 0 (the trex coming to rest) and using the acceleration calculated in part a and the distance given to calculate v-final... however the answer that I get produces the wrong answer for the time... any suggestions?

 

[Fightfish]

Could you show your working? I'm a bit suspicious of the variables that you are using - they seem to be mixed up, especially d, which according to the question is the distance through which it freely falls before it gets decelerated, and not the distance traveled during the deceleration.
You should have two sets of equations, one to determine the velocity of the torso upon impacting the ground, and the second to determine the time taken to bring it to rest.