A stone A is dropped from rest down a well


A stone A is dropped from rest down a well, and in 1 s another stone B is dropped from rest. Determine the distance between the stones another second later.

A stone A is dropped from rest down a well

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Solution:

Show me the final answer↓

We will calculate the distance the first stone travels in 2 seconds, and we will calculate the distance the second stone traveled in 1 second. We will then subtract the difference to figure out the distance between them. To do so, we will use the following equation:

s_2=s_1+v_1t+\dfrac{1}{2}a_ct^2

(Where s_2 is final displacement, s_1 is initial displacement, v_1 is initial velocity, t is time, and a_c is constant acceleration)

 

From the question, we know the following:

s_1=0 ft

v_1=0 ft/s

a_c=32.2 ft/s^2

t=2 s (For the first stone)

t=1 s (For the second stone)

 

Let us use our equation to calculate the distance the first stone traveled.

s_2=s_1+v_1t+\dfrac{1}{2}a_ct^2

s_2=0+0+\dfrac{1}{2}(32.2)(2^2)

s_2=64.4 ft

 

Now, we will calculate the distance the second stone traveled.

s_2=s_1+v_1t+\dfrac{1}{2}a_ct^2

s_2=0+0+\dfrac{1}{2}(32.2)(1^2)

s_2=16.1 ft

 

We can now calculate the difference between the two:

\Delta s=64.4-16.1=48.3 ft

 

Final Answer:

The difference between the stones is 48.3 ft.

 

This question can be found in Engineering Mechanics: Dynamics, 13th edition, chapter 12, question 12-6.

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