From her bedroom window a girl drops a water-filled balloon to the ground, 4.75 m below. If the balloon is released from rest, how long is it in the air?
h=1/2 g t^2 solve for t.
To determine how long the water-filled balloon is in the air after being dropped from a bedroom window, we can use the equations of motion and apply the concept of free fall.
First, let's consider the initial vertical velocity (u) of the balloon when it is released. Since it is released from rest, the initial velocity is zero (u = 0).
Next, we need to determine the final vertical displacement (h) of the balloon, which is the distance between the girl's bedroom window and the ground. In this case, the displacement is given as 4.75 meters (h = 4.75 m).
Using the equation of motion for vertical displacement, we have:
h = ut + (1/2)gt^2
Where:
h = vertical displacement (4.75 m)
u = initial vertical velocity (0 m/s)
g = acceleration due to gravity (-9.8 m/s^2)
t = time of flight
Since the initial velocity (u) is zero, the equation simplifies to:
h = (1/2)gt^2
Substituting the given values:
4.75 = (1/2)(-9.8)t^2
Next, we can solve the equation for time (t). Rearranging the equation:
t^2 = (4.75 x 2) / 9.8
t^2 = 0.969
t ≈ √0.969
t ≈ 0.984 seconds (rounded to three decimal places)
Therefore, the water-filled balloon will be in the air for approximately 0.984 seconds after being dropped from the bedroom window.