Question

A stone is dropped from a helicopter hovering at a constant height of 490m. How long before the stone reaches the ground?

Answer 1

It takes `10s` for the stone to reach the ground.

Explanation:

Well, you know that the gravitational force of the Earth is 9.8m/ `s^2`. Therefore acceleration is `9.8m/ s^2` or `-9.8m/ s^2`. The negative sign means the direction (if we set down as positive then we would use positive `9.8m/ s^2` and if we set up as positive then our acceleration would be negative). In this case, you would get a positive answer anyways as we are trying to find time.

We also know that the initial velocity of the object is 0m/s. And the displacement is 490m.

Most likely you know the big five equations of kinematics. In this example, we would use this equation:
`Deltad=V_"initial"*t +1/2at^2`

Wee can now substitute in out givens and solve for `t`:
`490m=0+1/2(9.8m/s^2)t^2`

`(490m)/(4.9m/s^2)=t^2`

`100s^2=t^2`

`sqrt(100s^2)=sqrt(t^2)`

`10s=t`

Therefore, It takes `10s` for the stone to reach the ground.

Please note that when you take a square root of something you get a positive and a negative answer. It wouldn't make sense for time to be negative so we pick the positive answer.