one of the fireworks is launched from the top of the building with an initial upward velocity of 150 ft/sec
One of the fireworks is launched from the top of the building with an initial upward velocity of 150 ft/sec.
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To calculate the height of the fireworks launched from the top of a building with an initial upward velocity of 150 ft/sec, you need to consider the acceleration due to gravity.
Step 1: Determine the acceleration due to gravity (g)
The acceleration due to gravity is approximately 32 ft/sec^2.
Step 2: Find the time taken for the firework to reach its peak height.
To reach its peak height, the firework's vertical velocity will decrease until it becomes zero. At this point, it starts falling back down due to gravity. The time taken to reach the peak can be found using the equation:
v = u + at
Where:
v = final velocity (0 ft/sec at peak)
u = initial velocity (150 ft/sec)
a = acceleration (-32 ft/sec^2)
t = time
Rearranging the equation and substituting the given values:
0 = 150 ft/sec + (-32 ft/sec^2) * t
Solving for t:
t = -150 ft/sec / -32 ft/sec^2
t ≈ 4.69 seconds
Step 3: Calculate the maximum height reached.
The maximum height can be found by calculating the displacement from the ground using the equation:
s = ut + (1/2) * a * t^2
Where:
s = displacement (maximum height)
u = initial velocity (150 ft/sec)
a = acceleration (-32 ft/sec^2)
t = time (4.69 seconds)
Substituting the values into the equation:
s = (150 ft/sec) * (4.69 seconds) + (1/2) * (-32 ft/sec^2) * (4.69 seconds)^2
Simplifying:
s ≈ 703.5 feet
Therefore, the height of the firework at its peak is approximately 703.5 feet.