From her bedroom window a girl drops a water-filled balloon to the ground, 4.94 m below. If the balloon is released from rest, how long is it in the air?
Given:
s(0) = 0
v(0) = 0
s(t) = -4.94m
g = -9.8m/s²
Use the equation to solve for t.
s(t) = s(0) + v(0) t + ½ g t²
To find the time the balloon is in the air, we can use the equation for the time it takes for an object to fall to the ground. This equation is derived from the equation of motion under constant acceleration:
h = (1/2) * g * t^2
Where:
h = distance fallen (4.94 m in this case)
g = acceleration due to gravity (9.8 m/s^2 on Earth)
t = time the balloon is in the air (unknown)
Rearranging the equation to solve for t, we get:
t^2 = (2 * h) / g
Substituting the known values, we have:
t^2 = (2 * 4.94) / 9.8
t^2 = 0.998
t ≈ √0.998
t ≈ 0.999
Therefore, the time the balloon is in the air is approximately 0.999 seconds.