When jumping straight down, you can be seriously injured if you land stiff-legged. One way to avoid injury is to bend your knees upon landing to reduce the force of the impact. A 75 kg man just before contact with the ground has a speed of 6.1 m/s. (a) In a stiff-legged landing he comes to a halt in 2.5 ms. Find the average net force that acts on him during this time. (b) When he bends his knees, he comes to a halt in 0.12 s. Find the average force now

To solve this problem, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.

Given:
Mass of the man (m) = 75 kg
Initial speed (v) = 6.1 m/s
Time for stiff-legged landing (t1) = 2.5 ms = 0.0025 s
Time for bend-knees landing (t2) = 0.12 s

(a) Stiff-legged landing:
To find the average net force, we need to determine the acceleration (a) first.

Using the equation:
v = u + at, where
v = final velocity = 0 m/s (since the man comes to a halt)
u = initial velocity = 6.1 m/s
t = time taken = 0.0025 s

Rearranging the equation, we get:
a = (v - u) / t

Substituting the given values, we have:
a = (0 - 6.1) / 0.0025

Calculating the acceleration:
a = -2440 m/s²

Now, we can use Newton's second law to find the average net force:
F = m * a

Substituting the values:
F = 75 * -2440

Calculating the average net force acting on the man during this time:
F = -183,000 N

(b) Bend-knees landing:
We follow the same approach as in part (a), but with a different time.

Using the equation v = u + at:
a = (0 - 6.1) / 0.12

Calculating the acceleration:
a = -50.833 m/s²

Using Newton's second law:
F = m * a

Substituting the values:
F = 75 * -50.833

Calculating the average net force acting on the man during this time:
F = -3812 N

Therefore, the average net force during the stiff-legged landing is -183,000 N, and during the bend-knees landing is -3812 N. Note that the negative sign indicates that the force is acting in the opposite direction to the motion of the man.

To find the average net force acting on the person in both cases, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

(a) In the case of a stiff-legged landing, the person comes to a halt in 2.5 ms (which is equivalent to 0.0025 s). We need to calculate the acceleration to find the net force.

Using the equation of motion: v = u + at, where v is the final velocity (0 m/s in this case), u is the initial velocity (6.1 m/s in this case), a is the acceleration, and t is the time.

Rearranging the equation to solve for acceleration, we have: a = (v - u) / t

Substituting the given values, we get: a = (0 - 6.1) / 0.0025
a = -2440 m/s² (negative sign indicates deceleration)

Now, we can calculate the average net force using Newton's second law: F = m * a

Substituting the person's mass of 75 kg and the calculated acceleration of -2440 m/s², we get: F = 75 kg * (-2440 m/s²)
F ≈ -183,000 N

Therefore, in the stiff-legged landing, the average net force acting on the person is approximately -183,000 N.

(b) In the case where the person bends their knees, they come to a halt in 0.12 s. Similar to the previous case, we calculate the acceleration first.

Using the equation of motion: a = (v - u) / t

Substituting the given values, we get: a = (0 - 6.1) / 0.12
a ≈ -50.8 m/s²

Now, we can calculate the average net force using Newton's second law: F = m * a

Substituting the person's mass of 75 kg and the calculated acceleration of -50.8 m/s², we get: F = 75 kg * (-50.8 m/s²)
F ≈ -3,810 N

Therefore, when the person bends their knees upon landing, the average net force acting on them is approximately -3,810 N.