A ball is dropped from rest off a 31 m building. How long does it take to hit the ground at the bottom of the building?
To calculate the time it takes for the ball to hit the ground, we can use the kinematic equation for vertical motion. The equation is:
s = ut + (1/2)gt^2
Where:
s is the distance (in this case, the height of the building) - 31 m.
u is the initial velocity - 0 m/s (since the ball is dropped from rest).
g is the acceleration due to gravity - approximately 9.8 m/s^2.
t is the time we want to find.
Rearranging the equation to solve for time, we have:
t^2 = (2s)/g
Substituting the given values:
t^2 = (2 * 31 m) / (9.8 m/s^2)
t^2 = 62 m / 9.8 m/s^2
t^2 ≈ 6.3265 s^2
Taking the square root of both sides, we can find t:
t ≈ √6.3265
t ≈ 2.51 s
Therefore, it takes approximately 2.51 seconds for the ball to hit the ground at the bottom of the building.