Question

Two identical objects A and B fall from rest from different heights to the ground. If object B takes twice as long as A to reach the ground, what is the ratio of the heights (A:B) from which the two objects fell? Neglect air resistance.

Answer 1

D = Vit + 1/2at^2
Falling from rest would remove Vit (Initial Velocity * time)
D = 1/2at^2
D/t^2 = 1/2a (in this case a= acceleration = gravity = 9.8 m/s^2
D/t^2 = 4.9 m/s^2
D = 4.9 m/s^2 * t^2

For object A, lets imagine t = 1
and for object B, lets imagine t = 2

for a: D = 4.9 m/s^2 * 1s^2
D = 4.9 m/s^2 * 1s^2
D = 4.9m

for b: D = 4.9 m/s^2 * 2s^2
D = 4.9 m/s^2 * 4s^2
D = 19.6m

4.9m/19.6m = .25

Ratio a/b: .5

Answer 2

1.1:4
2. 1:2
3.1:8
4. 1:squareroot 2

Answer 3

@greenleaf800073 you're missing a 2

Answer 4

@k1112
It would be A, 1:4

Answer 5

4.9m/19.6m = .25

Ratio a/b: .\(\color {red}{\bf 2}\)5