Two diamonds begin a free fall from rest from the same height, 1 s apart. How long after the first diamond begins to fall will the two diamonds be 10 m apart?
The part that confuses me is when the diamonds are 1s apart.
s=(-1/2)g*t^2
At t=1sec the first one has fallen 4.9m and the diamods are only 4.9m apart. At t=2sec the first one has fallen 19.6m and the second has fall 4.9m and they are 14.7m apart. Thus your time should be between 1 and 2 seconds, right? Now try to work it.
To find the time at which the two diamonds will be 10 m apart, we need to consider the relative motion between them. Let's break it down step by step:
1. First, we need to calculate the distance fallen by each diamond after time t from the start of the first diamond's fall.
- The formula for the distance fallen by an object in free fall is given by s = (1/2)gt^2, where s is the distance fallen, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time elapsed.
2. We know that the first diamond starts falling from rest, so after 1 second, it will have fallen a distance of s1 = (1/2)g(1^2) = 4.9 m.
3. Since the second diamond begins its free fall 1 second later, its distance fallen at time t will be less than that of the first diamond.
- Let's represent the distance fallen by the second diamond at time t as s2. Therefore, s2 = (1/2)g(t-1)^2, as it starts 1 second later than the first diamond.
4. We want to find the time when the two diamonds are 10 m apart. Thus, we can set up the equation s2 - s1 = 10 and solve for t.
- Substituting the values we know: (1/2)g(t-1)^2 - 4.9 = 10
- Simplifying the equation: (1/2)g(t-1)^2 = 14.9
5. Now, we solve the equation for t. First, multiply both sides of the equation by 2 to eliminate the fraction: g(t-1)^2 = 29.8.
6. Next, divide both sides of the equation by g: (t-1)^2 = 29.8/g.
7. Finally, take the square root of both sides to solve for t: t-1 = √(29.8/g).
8. To isolate t, add 1 to both sides of the equation: t = 1 + √(29.8/g). This gives you the time at which the two diamonds will be 10 m apart.
Note: Make sure to use the value of g in meters per second squared when performing the calculations.
By following these steps, you should be able to determine the time at which the two diamonds will be 10 m apart.