SOLUTION: Science and medicine. Find the time required for an object to fall to the ground from a building that is 1400 ft high. (Use this formula The time in seconds that it takes for an ob

Algebra ->  Radicals -> SOLUTION: Science and medicine. Find the time required for an object to fall to the ground from a building that is 1400 ft high. (Use this formula The time in seconds that it takes for an ob      Log On


   



Question 78051: Science and medicine. Find the time required for an object to fall to the ground from a building that is 1400 ft high. (Use this formula The time in seconds that it takes for an object to fall from rest is given by t=1/4 √s in which s is the distance fallen.)This is suppose to be a radical sign √ but this is as close as I could get.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
note: to write the radical sign sqrt%28x%29 write sqrt(x) and surround it by three { curly brackets on both sides (use the other curly bracket } for the right side) Click "view source" to see what I'm talking about.

To find the time, simply plug in s=1400.
t=%281%2F4%29%2Asqrt%281400%29
If we list all the factors of 1400 we get:

1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400


Notice the largest perfect square is 100, so rewrite 1400 as 100*14
t=%281%2F4%29%2Asqrt%28100%2A14%29

t=%281%2F4%29%2Asqrt%28100%29%2Asqrt%2814%29 Rewrite the equation using sqrt%28xy%29=sqrt%28x%29sqrt%28y%29

t=%281%2F4%29%2A10%2Asqrt%2814%29 Reduce

t=%2810%2F4%29%2Asqrt%2814%29 Multiply

t=%285%2F2%29%2Asqrt%2814%29 Reduce the fraction
So this is the exact time that it takes to fall. The approximate time is about 9.35414 seconds