A stone is dropped from the roof of a high building. A second stone is dropped 1.51 later. How far apart are the stones when the second one has reached a speed of 12.6 ?
Second Stone:
d = (V^2-Vo^2)/2g.
d = (158.76-0)/19.6 = 8.1 m.
Tf = (V-Vo)/g = (12.6-0)/9.8 = 1.29 s. =
Fall time.
First Stone:
Tf = 1.51 + 1.29 = 2.80 s.
d = Vo*t + 0.5g*t^2.
d = 0 + 4.9*2.8^2 = 38.3 m.
D = 38.3 - 8.1 = 30.2 Meters apart.
To determine the distance between the stones when the second one reaches a speed of 12.6 m/s, we need to calculate the distance traveled by each stone during the time interval of 1.51 seconds.
First, let's find the distance traveled by the second stone during this time interval. We can use the equation of motion:
d = v * t
where d represents the distance, v is the velocity, and t is the time.
Given that the velocity of the second stone is 12.6 m/s and the time is 1.51 seconds, we can substitute these values into the equation:
d2 = 12.6 * 1.51
Calculating this gives us:
d2 = 19.026 meters
Therefore, the second stone travels a distance of 19.026 meters during the 1.51-second time interval.
Now, to find the distance between the stones, we need to determine the distance traveled by the first stone during the same time interval. The first stone has been dropping for a longer duration, so we can calculate its distance using the equation of motion again:
d1 = (1/2) * g * t^2
where d1 represents the distance, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
Plugging in the values:
d1 = (1/2) * 9.8 * (1.51)^2
Calculating this gives us:
d1 ≈ 11.104 meters
Therefore, the first stone travels a distance of approximately 11.104 meters during the 1.51-second time interval.
To find the distance between the stones, we subtract the distance traveled by the first stone from the distance traveled by the second stone:
distance between stones = d2 - d1
Substituting the values we calculated:
distance between stones = 19.026 - 11.104
Calculating this gives us:
distance between stones ≈ 7.922 meters
Therefore, the distance between the two stones when the second stone has reached a speed of 12.6 m/s is approximately 7.922 meters.