From her bedroom window a girl drops a water-filled balloon to the ground, 4.3 m below. If the balloon is released from rest, how long is it in the air?
How would you do this?
2.9
To calculate the time it takes for the water-filled balloon to reach the ground when released from rest, we can use the principles of free fall. Here's how you can do it:
1. Determine the initial height: The question states that the girl drops the balloon from her bedroom window, which is 4.3 m above the ground. This is the initial height (h) of the balloon.
2. Use the formula for free fall: The equation that describes the height (h) of an object in free fall as a function of time (t) is given by:
h = (1/2) * g * t^2
Where g is the acceleration due to gravity, which is approximately 9.8 m/s^2 on Earth.
3. Rearrange the equation: Since the balloon is released from rest, its initial velocity (v0) is 0 m/s. Therefore, we can simplify the equation to calculate time:
h = (1/2) * g * t^2
4.3 = (1/2) * 9.8 * t^2
8.6 = 4.9 * t^2
4. Solve for time: To get the time, we need to solve the above equation for t. Divide both sides of the equation by 4.9:
(8.6 / 4.9) = t^2
1.755 = t^2
Then, take the square root of both sides to get the time (t):
t β β1.755
t β 1.32 seconds
Therefore, the water-filled balloon will be in the air for approximately 1.32 seconds before it hits the ground.
I would take the equation
Y = (g/2)*T^2 = 4.3 m
and solve it for T.
g is the acceleration of gravity and T is the time in the air.
You must have seen this equation before, for the distance that a dropped object falls in time T