SOLUTION: Hello. I have come requesting help for the following quadratic word problem: "Suppose one object is dropped from a height of 100 feet while another is dropped from 200 feet. Does

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Hello. I have come requesting help for the following quadratic word problem: "Suppose one object is dropped from a height of 100 feet while another is dropped from 200 feet. Does       Log On


   

Question 777701: Hello. I have come requesting help for the following quadratic word problem:
"Suppose one object is dropped from a height of 100 feet while another is dropped from 200 feet. Does it take twice as long for the higher object to hit the ground?"
I have used the formula h%28t%29=+-16t%5E2+%2BV%28t%29%2Bh in my attempts to solve it, but as the value of V (Initial Velocity) is not provided, my attempts have been fruitless. Any help would be very appreciated, and many thanks in advance to anyone who can help.


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
There is no initial velocity since the object,
So the equation reduces to:
+h%28t%29+=+-16t%5E2+%2B+h+
--------------------
I need to find the time interval when
+h+ goes from +h+=+100+ to +h+=+0+
and then when
+h+ goes from +h+=+200+ to +h+=+0+
---------------------------------------
+h+=+100+ at +t+=+0+
+h%5B0%5D+=+-16%2A0%5E2+%2B+100+
and
+h%5Bt%5D+=+0+ ( when object hits ground )
+0=+-16t%5E2+%2B+100
+16t%5E2+=+100++
+t%5E2+=+100%2F16+
+t+=+10%2F4+ sec
------------------
+h+=+200+ at +t+=+0+
+h%5B0%5D+=+-16%2A0%5E2+%2B+100%0D%0Aand%0D%0A%7B%7B%7B+h%5Bt%5D+=+0+ ( when object hits ground )
+0=+-16t%5E2+%2B+200
+16t%5E2+=+200++
+t%5E2+=+200%2F16+
+t+=+%2810%2F4%29%2Asqrt%282%29+ sec
-----------------------
The ratio of the times is:
+%28%2810%2F4%29%2Asqrt%282%29%29+%2F+%28+10%2F4+%29+=+sqrt%282%29+
The object does not take twice as long
to reach the ground. It take 1.414 times as long