I need a formula to calculate the height in ft from which something would have to fall to reach a certain mph?

Question

This formula could demonstrate the height (in feet) from which a person would have to fall to hit their head in a car crash at say 2, 5 or 10 mph.

Answer 1

When you drop something its potential energy is converted to kinetic energy. So assign the value of 1 unit to the mass then calculate the kinetic energy at the desired speed. Then calculate what height provides that much potential energy.

Answer 2

This is a great example why America should convert to metric. It would make this far far easier to calculate.

Ok lets do it anyway.

2as = v^2 - u^2
a is acceleration, s is distance, v is final velocity, u is inital velocity.
s = v^2 / 2g where g is gravity.
Now to include all the yucky imperial measurements.
g is 32.15ft / s^2
= 0.00609 miles / s^2
= 79000 miles / h^2
So s = 5480 * v^2 / 79000
s = 0.067 v^2
where s is in feet and v is in mph.

Answer 3

Physics is fun isnt it.

You want the velocity. But you are not looking for mph you are looking for m/s (thats meters per second).

The equation is v = d/t

v = velocity
d= displacement
t = time in seconds

Velocity is the displacement divided by the time in seconds.


Ex: 10 meters displacement divided by 2 seconds is a velocity of 5m/s.

Hope this helps.

Answer 4

the only force that acts is the gravitational force
you have then the gravitational acceleration g
a=g, integrate it
v(t) = v_0 + tg, integrate again

h(t) = h_ 0 + v_0 t + t^2/2 g,
where v_0 is the initial velocity and h_0 is the initial height.

Answer 5

something falls at a rate of 9.8 meters per second square,or in feet 32.15223 feet per second square