Help with free falling physics?

Question

I don't know what formulas and processes to use with this question.

A person drops a stone from rest into a hole. The speed of sound is 343 m/s in air, and the sound is heard 1.5 s after the drop. How deep is the hole?

Answer 1

Assume no air resistance and assume that they didn't throw the rock to give it an initial velocity.

The general formula is:

d = d(0) + v(0) + 1/2 at^2

In this case, d(0) = 0 and v(0) = 0 so we just have:

d = 1/2 a t^2

d = 4.9 (1.5)^2

d = 4.9 * 2.25

or, 11.025 meters deep. I worked the problem as if acceleration due to gravity was in the positive direction. So, the answer we get is positive and it means 11.025 down.

Answer 2

You've got to do this problem in two parts. First part is stone falling, second part is sound traveling at a constant speed from the bottom of the well to your ears.

First find the time, t, it takes for a stone to fall y meters
y = (gt^2)/2, solve for t in terms of y

Second, find the time, t2, it takes for the sound to travel y meters - this should be easy, and again solve for t2 in terms of y.

Last (ok, 3 steps instead of 2, sorry :-) combine the two equations you made in the first two parts and solve for y, since now you know that t + t2 = 1.5 seconds.

Answer 3

h=g*(t1)^2/2 distance the stone travels in time t1
h=v*(t2) distance the sound travels it time t2
t1 + t2 = t ; t=1.5 s given in the problem

Solve for t1 and t2: (use first two)
Use these 3 eqns to find h


The answer above is close enough, to zeroth degree approximation, but not absolutely accurate. The idea it right. Now you can work it out.

Answer 4

Pls study about speed,displacement,velocity acceleration ,distance travelled etc
v=u+at,
s=ut+1/2 at^2
v^2-u^2=2as
u=initial velocity
v=final velocity
a=acceleration
if it is replaced by g ie acceleration due to gravity
u can use these formulae for freely falling bodie
s-distance travelled and t-time

Answer 5

its 40 feet deep. speed of sound is negligible at such a distance. so the rock fell for 1.5 seconds. it accelerates 32 feet per second per second. so, the rock falls 16 feet the first second, and 24 feet the next half second. the rate of acceleration is steady