Calculating Cliff Height Using Acceleration Due to Gravity

[thschica]

A stone is dropped from the top of a cliff. It is seen to hit the ground below after 3.30 s. How high is the cliff?

 

[ZapperZ]

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Zz.

 

[Renge Ishyo]

This is a basic kinematics problem so it works the same mathematically as say the "car problem".

In the car problem, you can figure out the horizontal distance something travels using time by the relationship:

X = Vi(t) + 1/2(A)t^2

There are 4 variables in this equation: distance, velocity, time, and acceleration. If you know three of them, you can solve for the missing one. So let's say the car was initially at rest. Your initial velocity would be Vi = 0. Let's say the car accelerates at a constant rate of 4 m/s. Then A=4 m/s. And let's say that you want to know how far the car traveled in say 20 seconds. Now you know T. Once you know three of the 4, you can plug these in and use Algebra to solve for the missing distance traveled, X.

Your problem is very similar to the car problem except instead of a car traveling horizontally you have a ball traveling in a straight line vertically. Without spoiling anything you are given the time, the initial velocity, and the acceleration in your problem as well. Think about it a bit and you should be able to figure out what these three values are. From there, you can use the equation and solve.

 

[Sameer]

u = 0 -as it is dropped.
t = 3.3 secs.
height = s
a = acceleration due to gravity = 10 approx.
s = ut +1/2at^2 ( t^2 is t square i.e t to the power of 2)
s = 0 + 1/2 * 10 * 3.3*3.3
s = 5 * 10.9
s =54.5
Therefore the height of the cliff is 54.5 m.

 

[thschica]

I am still confused as to what exactly is the acceleration.I know the initial velocity is 0 and the time is 3.30 sec.But i don't know what the acceleration is!

 

[thschica]

Nevermind The acceleration is 9.80 thanks everyone for the help!

 

[ludi_srbin]

Well I hope you know what acceleration means. In this problem it equals to 9.81 m/s^2 (gravitation constant), and it is acceleration caused by gravity, because you are dropping the stone verticaly.