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 80.6-kg man just before contact with the ground has a speed of 6.59 m/s. (a) In a stiff-legged landing he comes to a halt in 3.82 ms. Find the magnitude of the average net force that acts on him during this time. (b) When he bends his knees, he comes to a halt in 0.206 s. Find the magnitude of the average net force now.
the man changed his velocity by 6.59 m/s in 3.92 ms, so his deceleration was
a = 6.59m/s / 0.00659s = 1000m/s^2
and, since F = ma, the force should now be obvious.
it is ...idk
To find the magnitude of the average net force acting on the man during a stiff-legged landing, we can use the impulse-momentum principle, which states that the change in momentum of an object is equal to the average force applied to it multiplied by the time interval over which the force is applied.
(a) In a stiff-legged landing, the man comes to a halt in 3.82 ms (milliseconds), which is equal to 3.82 × 10^-3 seconds.
The change in momentum of the man can be calculated using the equation:
Δp = m * Δv
where Δp is the change in momentum, m is the mass of the man, and Δv is the change in velocity.
Given that the mass of the man is 80.6 kg and the initial velocity is 6.59 m/s, the change in momentum is:
Δp = 80.6 kg * (0 m/s - 6.59 m/s) = -530.754 kg·m/s
Since force is defined as the rate of change of momentum, the average net force can be calculated by dividing the change in momentum by the time interval:
F = Δp / Δt
F = (-530.754 kg·m/s) / (3.82 × 10^-3 s) = -1.39 × 10^5 N
Therefore, the magnitude of the average net force during a stiff-legged landing is approximately 1.39 × 10^5 N.
(b) When the man bends his knees, he comes to a halt in 0.206 seconds.
Following the same procedure as above, the change in momentum is calculated as:
Δp = 80.6 kg * (0 m/s - 6.59 m/s) = -530.754 kg·m/s
The average net force is then given by:
F = Δp / Δt
F = (-530.754 kg·m/s) / (0.206 s) = -2.57 × 10^3 N
Therefore, the magnitude of the average net force when the man bends his knees is approximately 2.57 × 10^3 N.