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?

1 Answer
Apr 16, 2018

Answer:

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#