What Is the Average Force on a Parachutist's Feet When Landing Stiff-Legged?

[Killic]

Homework Statement

When a person parachutes, the impact velocity is equal to that attained in free fall from a height of 4.5 m. After contacting the ground, the jumper’s momentum is quickly brought to zero by the earth. Assuming that the person has a mass of 80 kg, what is the average force on the jumper’s feet if he lands stiff-legged and the impulse lasts only 0.019 s?

The Attempt at a Solution

v₂² = v₁² + 2aΔd
v₂² = (2)(1.8)(4.5)
v₂ = 9.4 m/s [down]

p = mv
p = (90)(9.4)
p = 752 N

F = Δp/Δt
F = 750/0.019
F = 3.9 × 10⁴ N [up]

However, the correct answer is 4.03 x 10⁴ N [up]. My teacher hinted towards the normal force to the person's weight is added to the answer. This confuses me as I thought that the impulse takes that into consideration already. Someone please help clarify this for me. Thanks in advance.

 

[NascentOxygen]

Hi Killic... http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

The answer you obtained (through omitting gravity) is the answer that applies if the problem was reworded for horizontal motion, viz., a speed skater comes off the rink at 9.4 m/sec and collides with a plasterboard-encased concrete wall, coming to a stop in 0.019 secs.

But it takes additional force to halt a body moving vertically because gravity is trying to accelerate the body (pulling downwards) all the time that friction (pushing upwards) is trying to slow the body.

 

[PeterO]

Homework Statement

When a person parachutes, the impact velocity is equal to that attained in free fall from a height of 4.5 m. After contacting the ground, the jumper’s momentum is quickly brought to zero by the earth. Assuming that the person has a mass of 80 kg, what is the average force on the jumper’s feet if he lands stiff-legged and the impulse lasts only 0.019 s?

The Attempt at a Solution

v₂² = v₁² + 2aΔd
v₂² = (2)(1.8)(4.5)
v₂ = 9.4 m/s [down]

p = mv
p = (90)(9.4)
p = 752 N

F = Δp/Δt
F = 750/0.019
F = 3.9 × 10⁴ N [up]

However, the correct answer is 4.03 x 10⁴ N [up]. My teacher hinted towards the normal force to the person's weight is added to the answer. This confuses me as I thought that the impulse takes that into consideration already. Someone please help clarify this for me. Thanks in advance.

Your teacher gave a good lead.
You have calculated the net Force on the jumper.
That is; the result after adding the upward force from the ground to the downward force due to gravity.