Help on this accelerated motion problem please

[black_hole]

Homework Statement

A stone is dropped from the roof of a high building. A second stone is dropped 1.31 s later. How far apart are the stones when the second stone has reached a speed of 19.3 m/s?

Homework Equations

well...

stone 1
V₀ = 0m/s
v_f = unknown
t = unknown
a = -9.8m/s/s
x = trying to find

stone 2
V₀ = 0m/s
v_f = 19.3m/s
t = unknown
a = -9.8m/s/s
x = trying to find

The Attempt at a Solution

That's all I know.

 

[rl.bhat]

For stone two, find t to reach the velocity 19.3 m/s.
Using the kinematic equation, find the displacement of stone 2.
Find the displacement of stone i in time ( t+1.31s )

 

[kerimek]

I would suggest the following steps to solve this accelerated motion problem:

1. Identify the known and unknown variables: In this problem, the known variables are the initial velocity (V0) and acceleration (a) for both stones, the time difference (t) between the two stones, and the final velocity (vf) for the second stone. The unknown variables are the final velocity (vf) for the first stone and the distance (x) between the two stones.

2. Use the equations of motion to solve for the unknown variables: The equations of motion for this problem are:

vf = V0 + at (for calculating final velocity)
x = V0t + 1/2at^2 (for calculating distance)

Using these equations, we can solve for the unknown variables vf and x for both stones.

3. Plug in the known values and solve for the unknown variables: Substituting the known values into the equations, we get:

For Stone 1:
vf = 0 + (-9.8)(t)
vf = -9.8t

For Stone 2:
19.3 = 0 + (-9.8)(t)
t = 19.3/-9.8
t = -1.97 seconds (Note: The negative sign indicates that the second stone is dropping downwards)

Now, using the value of t, we can solve for the distance (x) between the two stones:
x = 0 + 1/2(-9.8)(-1.97)^2
x = 19.2 meters

Therefore, the two stones are 19.2 meters apart when the second stone has reached a speed of 19.3 m/s.

4. Check your answer: To make sure that our answer is correct, we can use the equations of motion to check if the final velocity of the first stone is also 19.3 m/s when it reaches the ground. Using the value of t = -1.97 seconds, we get:

vf = 0 + (-9.8)(-1.97)
vf = 19.3 m/s

Thus, our answer is correct.

In conclusion, by using the equations of motion and the known values, we were able to solve for the unknown variables and determine the distance between the two stones when the second stone reaches a speed of 19.3 m/s. I hope this helps with your homework problem.