Gravity Brothers
Two brothers, known as the Gravity Brothers, hold a Youtube channel, showing what they did with gravity. One particular video shows them throwing an iPhone up in the air at 400 feet per second. The brother who throws it is throwing it to his brother on a podium 1600 feet above sea level. At first, the brother misses it, but on the way down, the brother catches the device, along with a voided warranty. How many seconds did it take for the 2nd brother on the podium to catch the iPhone?
Use the appropriate formula for each measurement system. In this case, use the feet formula.
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1 solution
Use the formula h = r t − 1 6 t 2 (for feet)
Let's plug in all the numbers for the formula.
Since the podium is 1600 ft high, h should equal 1600. We need to test the time it takes to reach 1600.
Since the rate at which the iPhone is going is 400ft/sec., r should equal 400.
It's L A T E X from now on until the logical part.
1 6 0 0 = 4 0 0 t − 1 6 t 2 Now transfer over the variables so we can factor it.
1 6 t 2 − 4 0 0 t + 1 6 0 0 = 0
Factor out 1 6 .
1 6 ( t 2 − 2 5 t + 1 0 0 = 0 )
Now factor.
1 6 ( t 2 − 2 5 t + 1 0 0 = 0 ) = 1 6 ( t − 5 ) ( t − 2 0 )
Our solutions are:
t = 5 o r 2 0
Now let's read the problem more. It says that he misses on the first try, but on the way down, he catches it. This is important.
The 5 seconds means, using common sense, the time taken to let the iPhone fly its way up.
The 20 seconds means, using common sense, the time take to let the iPhone fall on its way down .
Thus, since we want the time it takes to fall down, the solution is 2 0 seconds