# Free fall of a stone off a cliff

I am having trouble with this one. for all the formulas I tried I need the velocity, which they don't tell us in the problem. Any help would be appreciated .

A stone falls from rest from the top of a cliff.
A second stone is thrown downward from the
same height 2.4 s later with an initial speed of
47.04 m/s. They hit the ground at the same
time.
The acceleration of gravity is 9.8 m/s2 .
How long does it take the first stone to hit
the ground? Answer in units of s.

How high is the cliff? Answer in units of m.

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alphysicist
Homework Helper
Hi brendj3,

I am having trouble with this one. for all the formulas I tried I need the velocity, which they don't tell us in the problem. Any help would be appreciated .

A stone falls from rest from the top of a cliff.
A second stone is thrown downward from the
same height 2.4 s later with an initial speed of
47.04 m/s. They hit the ground at the same
time.
The acceleration of gravity is 9.8 m/s2 .
How long does it take the first stone to hit
the ground? Answer in units of s.

How high is the cliff? Answer in units of m.
What have you tried so far? They give some velocities in the problem, but until you show your work we can't know where you are getting stuck at.

ok what I did was

0 = -9.8 t + 47.04

where 47 is the initial velocity and 0 is the velocity i got a time of 4.8 sec. and then when added to the 2.4 it would give me 7.2 seconds, but I heard this answers was wrong. Do you know what the problem is?

gabbagabbahey
Homework Helper
Gold Member
ok what I did was

0 = -9.8 t + 47.04

where 47 is the initial velocity and 0 is the velocity i got a time of 4.8 sec. and then when added to the 2.4 it would give me 7.2 seconds, but I heard this answers was wrong. Do you know what the problem is?
You cannot assume that the velocity is zero as it hits the ground. At the instant the rock hits the ground, the rock will actually be traveling faster than its initial velocity since the acceleration due to gravity is in the same direction as the initial velocity. To solve this problem, you will actually need to solve two equations for t and h where h is the height of the cliff. Since you have two stones, both falling the same distance, h, but with different initial velocities it should be easy to get the two equations you need to solve...What is the height, y_1 of the first stone as a function of time? How about the height of the second, y_2?When are they equal?

LowlyPion
Homework Helper
ok what I did was

0 = -9.8 t + 47.04

where 47 is the initial velocity and 0 is the velocity i got a time of 4.8 sec. and then when added to the 2.4 it would give me 7.2 seconds, but I heard this answers was wrong. Do you know what the problem is?
What you calculated is the time it takes gravity to decelerate 47m/s to 0. This would be the time to max height if you threw the stone in the air at that speed. Interesting, but not necessarily useful.

Think about what you know. You know an initial velocity and a time delay and you are looking for the height of the cliff and time to the bottom.

What equation do you know that relates distance and initial velocity and time? That is the equation you should focus on.