A body is dropped from the rooftop of a building.The body reaches the ground at t= 4.05 from the point of release.How tall is the building?What is the speed of the body just before it reaches the ground?
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To determine the height of the building, we can use the equation of motion for a freely falling body. The equation can be written as:
h = 0.5 * g * t^2
where:
h = height of the building
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time taken to reach the ground (4.05 seconds in this case)
Substituting the given values into the equation:
h = 0.5 * 9.8 * (4.05)^2
h = 0.5 * 9.8 * 16.4025
h ≈ 80.13 meters
The height of the building is approximately 80.13 meters.
To calculate the speed of the body just before it reaches the ground, we can use another equation of motion:
v = g * t
where:
v = speed of the body
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time taken to reach the ground (4.05 seconds in this case)
Substituting the given values into the equation:
v = 9.8 * 4.05
v ≈ 39.69 m/s
The speed of the body just before it reaches the ground is approximately 39.69 m/s.