Two Diamonds begin a free fall from rest from the same height, 1.0 s apart. How long after the first diamond begins to fall will the two diamonds be 10m apart?
Please help, I am very confused with this question, I have completed all other but I am unsure about how to answer this. Any help is greatly appreciated!
d1 = Vo*t + (g/2)t^2. Vo = 0.
d1 = (g/2)t^2.
d2 = (g/2)(t-1)^2.
d1 = d2 + 10.
(g/2)t^2 = (g/2)(t-1)^2 + 10,
4.9t^2 = 4.9(t-1)^2 + 10,
4.9t^2 - 4.9(t-1)^2 = 10,
divide both sides by 4.9:
t^2 - (t-1)^2 = 2.04,
t^2 - (t^2-2t+1) = 2.04,
t^2 - t^2 + 2t - 1 = 2.04,
2t - 1 = 2.04,
2t = 3.04,
t = 1.52s.
To answer this question, you need to understand the concept of free fall and apply the equations of motion. Here's how you can approach it step by step:
1. Identify the given information:
- The height from which both diamonds start their free fall (which is not mentioned) is assumed to be the same.
- The time difference between the start of the two falls is given as 1.0 s.
- The distance between the two diamonds when we want to find the time is given as 10 m.
2. Free fall motion:
In free fall, an object only experiences the force of gravity, which accelerates it downward. The acceleration due to gravity on Earth is approximately 9.8 m/s².
3. Equations of motion for free fall:
In this case, we will use the equation:
d = ut + (1/2)at²
where:
- d is the distance traveled
- u is the initial velocity
- t is the time taken
- a is the acceleration
4. Analysis:
- For the first diamond, since it starts from rest, its initial velocity (u1) is 0 m/s.
- For the second diamond, since it starts 1.0 s later, its initial velocity (u2) is also 0 m/s.
- The distance traveled by the first diamond is d1 = ut1 + (1/2)at1².
- The distance traveled by the second diamond is d2 = ut2 + (1/2)at2².
5. Calculate the distance traveled:
Both diamonds start from the same height, so d1 = d2.
Therefore, we have: ut1 + (1/2)at1² = ut2 + (1/2)at2².
6. Determine the time when the distance between the two diamonds is 10 m:
Using the equation from step 5, substitute the given distance of 10 m for d1 and d2. Solve for t.
7. Solve for t:
After substituting all known values, you will obtain an equation with a quadratic term. Solve this equation to find the value of t.
8. Finalize the answer:
Once you solve the quadratic equation, you will find the time it takes for the given distance to be covered by both diamonds.
Remember to apply the correct units throughout the calculations. By following these steps, you should be able to find the time when the two diamonds are 10 m apart during their free fall.