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
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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) (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:
in this problem x=t; a=8; b=550; c=-2475
:
:
:
we only want the positive solution here
t =
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?
