I have to figure out the velocity for this problem to find the momentum but I can't seem to figure it out. I tried using gravity to find the time with 9.8 m/s^2 so I could find the velocity, but my answer is wrong:
Problem: A person can just survive a full-body collision (either to the front, back, or side) at roughly 9 m/s (20 mi/h) with an impact time of approximately 10 ms. At greater speeds or shorter times, fatal brain damage will likely occur. Could someone survive a fall from a 3.6 m landing flat on his or her back on soft soil so that s/he decelerates to rest through a distance of 8 cm (that's the total compression of the body and soil)? (Hint: survival depends on the magnitude of the deceleration, not on the impact time.)
If his or her mass is 75 kg, what's the impulse exerted on his or her body by the ground? Assume the deceleration is constant.
Problem: A person can just survive a full-body collision (either to the front, back, or side) at roughly 9 m/s (20 mi/h) with an impact time of approximately 10 ms. At greater speeds or shorter times, fatal brain damage will likely occur. Could someone survive a fall from a 3.6 m landing flat on his or her back on soft soil so that s/he decelerates to rest through a distance of 8 cm (that's the total compression of the body and soil)? (Hint: survival depends on the magnitude of the deceleration, not on the impact time.)
If his or her mass is 75 kg, what's the impulse exerted on his or her body by the ground? Assume the deceleration is constant.
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Break the problem up into two parts.
First use your third kinematics eq to find the persons velocity just before impact, as he falls h=3.6m under acceleration of gravity;
v = SqRt(2gh)
In the second part you use the same kinematics eq, where now the above "v" is the initial velocity and the distance traveled is y=.08m, and you want to find the deceleration "a";
a = v^2/2y
To see if the person survives you compare "a" to the given threshold acceleration of 9/.01 = 900m/ss
If "a" is less then 900m/ss you can survive.
The impulse is the change in momentum. So just multiply the "v" found above by the person's mass.
First use your third kinematics eq to find the persons velocity just before impact, as he falls h=3.6m under acceleration of gravity;
v = SqRt(2gh)
In the second part you use the same kinematics eq, where now the above "v" is the initial velocity and the distance traveled is y=.08m, and you want to find the deceleration "a";
a = v^2/2y
To see if the person survives you compare "a" to the given threshold acceleration of 9/.01 = 900m/ss
If "a" is less then 900m/ss you can survive.
The impulse is the change in momentum. So just multiply the "v" found above by the person's mass.