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How to Calculate Free Falling Problems

Newton's laws of motion dictate that mass is not a factor in an object's free-falling path. The traditional model holds that, in a vacuum, a feather will fall to the ground just as quickly as a bowling ball will. In order to calculate how long an object will take to reach the ground -- whether catapulted as a projectile or dropped from a stationary position -- you will need to know the acceleration due to gravity.

Things You'll Need

Pencil
Paper

Instructions

- 1
  Calculate a dropped object's velocity given a hang time of 6 seconds. This can be solved using the equation v=vi+at where vi is the initial velocity, a is the acceleration due to gravity, and t is the time spent in motion. In this case, vi is 0 since it was dropped, t is 6 seconds, and a is the acceleration due to gravity, which is 9.8 meters per second squared on earth, giving a velocity of 0 + (6)(9.8), or 58.8 meters per second.
- 2
  Find the acceleration due to gravity on a planet that takes 10 seconds for an object to travel 60 feet in a free fall without any air resistance. Use the equation x=xi+vi(t) + (1/2)(a)(t)^2, substituting 60 for (x-xi) and 10 for t. This will give you a=2(60 - (0)(10))/(10^2) = 120/100 = 1.2 feet per second squared.
- 3
  Calculate how long it will take for a pencil to fall off of a desk that is 1 meter high. Use the equation x = xi + vi(t) + (1/2)(a)(t)^2, substituting 1 for (x-xi) and 9.8 for a. This leaves you with t = ((1)(2)/(9.8))^(1/2) = 0.45 seconds.
- 4
  Calculate an object's initial speed if it was thrown straight upwards and travels to a height of 50 meters in 4 seconds. Use the equation x=vi(t) + (1/2)(a)(t)^2, substituting 50 for x, 4 for t, and 9.8 for a. This leaves you with vi= (50-(1/2)(9.8)(4)^2)/4 = 30.4 meters per second.

Nature