A snowball is launched horizontally from the top of a building at [tex]v = 16.9 \, \text{m/s}[/tex]. If it lands [tex]d = 44 \, \text{meters}[/tex] from the bottom, how high (in meters) was the building?

The height of the building is approximately 33.25 meters.
Calculating the height of the building:
Here's how to find the height of the building:

Define variables:

Initial horizontal velocity (v) = 16.9 m/s
Horizontal distance traveled (d) = 44 meters
Height of the building (h) - We need to find this

Use projectile motion equations:

Since the snowball is launched horizontally, its vertical motion is governed by free fall, with an acceleration of -g (negative due to downward direction).

Time of flight:

The time it takes for the snowball to reach the ground is the same as the time it takes for it to fall vertically from the top of the building. We can use the horizontal distance and velocity to find this time:
Time (t) = d / v
Time (t) = 44 meters / 16.9 m/s
Time (t) ≈ 2.60 seconds

Height using free fall equation:

Now, we can use the time and free fall equation to find the height:
h = 1/2 * g * t^2
h = 1/2 * 9.81 m/s^2 * (2.60 seconds)^2
h ≈ 33.25 meters
Therefore, the height of the building is approximately 33.25 meters.

Answered by bamkinbose | 2024-06-18

The height of the building from which the snowball is launched is approximately 33.25 meters. This is calculated using the time of flight and the free fall equation. The calculation considers the horizontal velocity and distance traveled by the snowball.
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Answered by bamkinbose | 2024-12-24