SOLUTION: Hi, I am having trouble with a word problem. The problem states "When a rock is dropped from a cliff into an ocean, it travels approximately 16t^2 ft in t seconds. If the splash is

Algebra ->  Equations -> SOLUTION: Hi, I am having trouble with a word problem. The problem states "When a rock is dropped from a cliff into an ocean, it travels approximately 16t^2 ft in t seconds. If the splash is      Log On


   

Question 221662: Hi, I am having trouble with a word problem. The problem states "When a rock is dropped from a cliff into an ocean, it travels approximately 16t^2 ft in t seconds. If the splash is heard 4.5 seconds later and the speed of sounds is 1100ft/sec, approximate the height of the cliff."
Thanks in advance.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
When a rock is dropped from a cliff into an ocean, it travels approximately 16t^2 ft in t seconds.
If the splash is heard 4.5 seconds later and the speed of sounds is 1100ft/sec, approximate the height of the cliff."
:
t = time for the rock to reach the water
then
(4.5-t) = time for the sound to reach the top of the cliff
:
Both the rock and the sound will travel the same distance.
Write a distance equation
:
16t^2 = 1100(4.5-t)
16t^2 = 4950 - 1100t
:
Arrange as a quadratic equation
16t^2 + 1100t - 4950 = 0
;
Simplify, divide by 2
8t^2 + 550t - 2475
:
Use the quadratic formula to find t:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
in this problem x=t; a=8; b=550; c=-2475
t+=+%28-550+%2B-+sqrt%28+550%5E2+-+4+%2A+8+%2A-2475+%29%29%2F%282%2A8%29+
:
t+=+%28-550+%2B-+sqrt%28302500+-+%28-72900%29+%29%29%2F%2816%29+
:
t+=+%28-550+%2B-+sqrt%28302500++%2B+72900+%29%29%2F%2816%29+
:
t+=+%28-550+%2B-+sqrt%28381700+%29%29%2F%2816%29+
we only want the positive solution here
t+=+%28-550+%2B+617.819%29%2F16+
t = 67.819%2F16
t = 4.239 sec for the rock to hit the water
and
4.5 - 4.238 = .261 sec for the sound to come back
:
:
You can use either value to find the height of the cliff
16(4.238^2) = 287 ft
and
1100(.261) = 287 ft
:
:
Make sense to you?