Final answer:
To find the time it takes for an object to hit the ground when released from a height of 7.88 meters, we use the kinematics equation for constant acceleration due to gravity. By substituting the given values and solving for time, we find that the object takes approximately 1.27 seconds to hit the ground.
Step-by-step explanation:
To calculate the time it takes for an object to hit the ground when released from rest at a given height, we can use the kinematics equation derived from the constant acceleration due to gravity, which is:
s = ut + (1/2)at²
Where:
- s = distance (height from which the object is released)
- u = initial velocity (which is 0 m/s since the object is released from rest)
- a = acceleration (which is the acceleration due to gravity, g = 9.8 m/s²)
- t = time (which is what we're trying to find)
Plugging in the given values and solving for t we get:
7.88 = 0·t + (1/2)·9.8·t²
Which simplifies to:
7.88 = 4.9t²
And then:
t² = 7.88 / 4.9
t² = 1.60816
t = sqrt(1.60816)
t ≈ 1.27 seconds
Thus, the object takes approximately 1.27 seconds to hit the ground.