Question

An object is thrown vertically from a height of `6 m` at `8 m/s`. How long will it take for the object to hit the ground?

Answer 1

About `2.19` seconds

Explanation:

Find the time it takes to reach the top of the projectile:

`t =(v_f-v_i)/g`

Knowing that at the top of the projectile the velocity is `0m/s`

`t= (-8m/s)/(-9.81m/s^2)=0.815 sec`

Using that time, we can also calculate the distance to the very top:

`vt= d= (4m/s)*(0.815 s)= 3.26 m`

So know we can know that the ball is a total of `6m +3.26= 9.26 m` off the ground, to calculate the time it takes for the ball to fall downward is:

`t = sqrt((2d)/g)`

`t= sqrt((2*9.26m)/(9.81m/s^2))= 1.374 s`

To find the total time of the ball in the air, just add the times:
`1.374s+0.815s= 2.19 sec`