# Find the speed with which the box hits the ground.

## Homework Statement

A box whose mass is 4kg is at rest on the floor. It is then lifted to a height of 2m by a constant a constant force F and then released. At this point the box has upward velocity of 5m/s. Do not use Newton's laws of motion to solve this problem.

A. Find magnitude of the force F
F=65N

B. Find the speed with which the box hits the ground.
???

g = 10m/s^2

## The Attempt at a Solution

A. Wother = ΔKE + ΔPE = 65N magnitude of force

B. 0 = 1/2mvf^2-1/2m(0)^2 + mg(0) - mghi
= 1/2mvf^2 - mghi
vf = √[(2*mghi)/m] = √2*4*10*2/4 = 6.32 m/s (WRONG)

The speed is supposed to be = 8.09 m/s
I just killed the constant force in the work and substituted in the values as if the box fell to ground. I don't know what i'm missing.

I will return soon.

TSny
Homework Helper
Gold Member
B. 0 = 1/2mvf^2-1/2m(0)^2 + mg(0) - mghi

Why zero here?

Last edited:
Why zero here?

I assumed it had to be zero for either final or initial velocity. so i can solve for v. i first tried vf = 0m/s to say the object has landed, and then i'd solve for vi with this formula.

1. The problem statement, all variables and given/known

## The Attempt at a Solution

A. Wother = ΔKE + ΔPE = 65N magnitude of force

B. 0 = 1/2mvf^2-1/2m(0)^2 + mg(0) - mghi
= 1/2mvf^2 - mghi
vf = √[(2*mghi)/m] = √2*4*10*2/4 = 6.32 m/s (WRONG)

The speed is supposed to be = 8.09 m/s
I just killed the constant force in the work and substituted in the values as if the box fell to ground. I don't know what i'm missing.

I will return soon.

When you solve for v...
0=½mv^2-mgh_i
½mv^2=mgh_i |:m |*2
v^2=2gh_i
v=√(2gh_i)

I assumed it had to be zero for either final or initial velocity. so i can solve for v. i first tried vf = 0m/s to say the object has landed, and then i'd solve for vi with this formula.

Why does one velocity have to be zero? You were given an initial velocity (vi=+5m/s), and you are told to find a final velocity (vf). By your logic, vf must be zero. This makes no sense for two reasons:
1. The ball is accelerating downwards, so as long as it starts from any height above the ground, it should have nonzero velocity when it hits the ground.
2. If you are told to find something, it is very rarely zero.