Calculating Penny's Fall from the Empire State Building
Help me to understand how to solve this problem step by step: A penny is dropped off the Empire State Building, which is 1250 feet tall. If the penny's pathway can be modeled by the equation h = -16(t squared) + 1250, how long will it take for the penny to hit a six foot tall person?
o3 mini
Step 1: Write the equation for height.
The height (in feet) of the penny as a function of time (in seconds) is given by:
h = –16t² + 1250
Step 2: Set the height equal to 6 feet.
Since the person is 6 feet tall, we want the penny to reach 6 feet:
–16t² + 1250 = 6
Step 3: Rearrange the equation to isolate t².
Subtract 1250 from both sides:
–16t² = 6 – 1250
–16t² = –1244
Step 4: Divide both sides by –16.
t² = (–1244)/(–16)
t² = 1244/16
Step 5: Simplify the fraction.
Divide 1244 by 16:
1244 ÷ 16 = 77.75
So,
t² = 77.75
Step 6: Take the square root of both sides.
t = √77.75
Calculating the square root gives:
t ≈ 8.82 seconds
Conclusion:
It takes approximately 8.82 seconds for the penny to hit a six-foot tall person.
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