Some people in a hotel are dropping water balloons from their window onto the ground below. The balloons take .15s to pass your 1.6m tall window. Where should security look for the raucous guest? Express your answer using tow significant figures.
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Well, security better start looking outside! But don't worry, with my impeccable calculations, I can help you find the height from which those water balloons are dropping.
Since it takes 0.15 seconds for the balloons to pass a 1.6m tall window, we can use a little bit of math to figure out their starting point.
First, we divide the height of the window (1.6m) by the time it takes for the balloons to pass (0.15 seconds). So, 1.6m / 0.15s = 10.6667m/s.
This means the balloons are falling at a rate of approximately 10.67 meters per second.
Therefore, security should look for the mischievous guest somewhere around 10.67 meters above the ground outside the hotel. But be careful, they might be floating away on a cloud of laughter!
To determine the position where security should look for the guest dropping water balloons, we can use the equation for free fall motion:
y = 0.5 * g * t^2
where:
y is the vertical position (height),
g is the acceleration due to gravity (approximately 9.8 m/s^2),
and t is the time taken for the balloon to pass the window (0.15 s).
Since the window height is 1.6 m, we can substitute these values into the equation to find the vertical position where the balloons are dropped:
y = 0.5 * 9.8 m/s^2 * (0.15 s)^2
Simplifying the equation:
y ≈ 0.11 m
Therefore, security should look for the raucous guest approximately 0.11 m below the window.
To determine where security should look for the raucous guest, we need to calculate the vertical distance covered by the water balloons during the time it takes to pass your window.
Given:
Height of the window = 1.6 m
Time taken to pass the window = 0.15 s
To solve this, we can use the formula for vertical displacement:
Vertical displacement = Initial velocity * time + (1/2) * acceleration * time^2
Since the water balloons are dropped, the initial velocity is 0 m/s, and the acceleration due to gravity is approximately -9.8 m/s^2 (the negative sign indicates downward direction).
Vertical displacement = 0 * 0.15 + (1/2) * (-9.8) * (0.15)^2
Vertical displacement = -0.11025 m
Since the displacement is negative, it means the water balloons fall below the window. To find the location where the balloons fall, we subtract the displacement from the height of the window.
Location of the raucous guest = Height of the window - Vertical displacement
Location of the raucous guest = 1.6 - (-0.11025)
Location of the raucous guest = 1.71025 m
Therefore, security should look approximately 1.71 m below the window to find the raucous guest.