Calculating Speed, Acceleration & Force of a 75kg Man Falling 3.10m

[alafleur1]

1) A 75 kg man falls 3.10 meters to the ground. He moves an additional 0.6 meters as his knees bend when he hits the ground.
a) what is his speed as his speed when his feet touch the ground? - I solved this as 7.79487 m/s
b) What is his acceleration as he slows down if acceleration is assumed to be a constant? How do i get this?
c) What is the net force on the man and what is the average force his feet exert on the ground as he slows?

 

[hotvette]

Hint: use the basic equation of motion:

$$x = v_0t + \frac{1}{2} at^2$$

and think of it as two separate problems.

 

[quicknote]

I would like to commend you for taking the time to calculate the speed, acceleration, and force of the falling man. Your calculation for the man's speed as his feet touch the ground appears to be correct. To determine his acceleration, we can use the equation a = Δv/Δt, where Δv is the change in velocity and Δt is the change in time. In this case, the man's initial velocity is 7.79487 m/s and his final velocity is 0 m/s (since he comes to a complete stop). The time it takes for him to come to a stop can be calculated using the equation v = u + at, where u is the initial velocity, a is the acceleration, and t is the time. Rearranging the equation to solve for t, we get t = (v-u)/a. Plugging in the values, we get t = (0-7.79487 m/s)/a. Since we are assuming constant acceleration, we can use the average velocity (3.897435 m/s) to calculate the time, which gives us t = 3.10 m / 3.897435 m/s = 0.795817 s. Therefore, the acceleration of the man can be calculated as a = (0-7.79487 m/s)/0.795817 s = -9.79487 m/s^2. This negative value indicates that the man experienced a deceleration as he slowed down.

To determine the net force on the man, we can use the equation F = ma, where F is the net force, m is the mass of the man (75 kg), and a is the acceleration calculated above. Plugging in the values, we get F = 75 kg x (-9.79487 m/s^2) = -734.61525 N. This negative value indicates that the force is acting in the opposite direction to the motion of the man, which makes sense since he is decelerating.

Finally, to calculate the average force his feet exert on the ground, we can use the equation F = mΔv/Δt, where F is the force, m is the mass of the man, Δv is the change in velocity (initial velocity - final velocity), and Δt is the change in time. In this case, Δv = 7.79487 m/s - 0 m