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

1 Answer

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.