A penny is dropped from rest from the top of the Trump Tower in New York City. Considering that the height of the building is 283 m and ignoring air resistance, find the speed with which the penny strikes the ground.
105.326 m/sec
MAGA
To find the speed with which the penny strikes the ground, we can use the principles of motion and gravitational acceleration.
Step 1: Determine the time it takes for the penny to fall.
We can use the formula for the time it takes for an object to fall freely from a certain height:
t = √(2h/g)
where:
t = time in seconds
h = height of the building (283 m)
g = acceleration due to gravity (approximately 9.8 m/s²)
Substituting the values into the formula:
t = √(2 * 283 / 9.8)
t ≈ 7.571 seconds
Step 2: Calculate the speed of the penny when it hits the ground.
We can use the formula for the final velocity of an object in free fall:
v = g * t
where:
v = final velocity
g = acceleration due to gravity (approximately 9.8 m/s²)
t = time to fall (7.571 seconds)
Substituting the values into the formula:
v = 9.8 * 7.571
v ≈ 74.078 m/s
Therefore, the speed at which the penny strikes the ground is approximately 74.078 m/s.