Answer:
The impulse when his legs hit the ground is approximately 359 N s
Explanation:
To calculate the impulse, we need to use the formula:
Impulse = change in momentum
Since the resident jumps from rest, his initial momentum is zero. We can calculate his final momentum using the formula:
p = m*v
where p is momentum, m is mass, and v is velocity.
p = 60 kg * 6 m/s = 360 kg m/s
Therefore, the change in momentum is:
Δp = final momentum - initial momentum = 360 kg m/s - 0 = 360 kg m/s
The impulse is equal to the change in momentum:
Impulse = Δp = 360 kg m/s
However, the question specifically asks for the impulse when his legs hit the ground. This means we need to consider the time it takes for his legs to come to a stop after hitting the ground. The impulse is given by:
Impulse = force x time
We can rearrange this formula to solve for time:
time = Impulse / force
To find the force, we can use the formula:
force = mass x acceleration
The resident is brought to a stop by the ground, so we can assume that the force exerted by the ground is equal to the resident's weight, which is:
force = mass x gravity
where gravity is the acceleration due to gravity, approximately 9.81 m/s².
force = 60 kg x 9.81 m/s² = 588.6 N
Now we can calculate the time it takes for the resident's legs to come to a stop after hitting the ground:
time = Impulse / force = 360 kg m/s / 588.6 N ≈ 0.61 s
Therefore, the impulse when his legs hit the ground is:
Impulse = force x time ≈ 588.6 N x 0.61 s ≈ 359 N s
So the impulse when his legs hit the ground is approximately 359 N s.