A Stone Of Mass 1kg Is Dropped From Rest From A Window 20m Above The Ground.Another Stone Of Mass 0.5kg Is Dropped From A Height Of 5m Above The Ground . If Both Stones Are Dropped At The Same Time,find The Time Interval That That Elapses Between The Two Stones Hitting The Ground.
t1 = sqrt(2* x1/g)
t2 = sqrt(2* x2/g)
diff = t1-t2
To find the time interval between the two stones hitting the ground, we can use the equation of motion:
h = ut + (1/2)gt^2
where:
h = height (distance fallen)
u = initial velocity (0 m/s for a stone dropped from rest)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time
For the first stone:
h1 = 20m (height)
u1 = 0 m/s (initial velocity)
g = 9.8 m/s^2 (acceleration due to gravity)
For the second stone:
h2 = 5m (height)
u2 = 0 m/s (initial velocity)
Let's calculate the time taken for each stone to hit the ground.
For the first stone:
h1 = u1t + (1/2)gt^2
20 = 0*t + (1/2)*9.8*t^2
20 = (4.9t^2)
t^2 = 20/4.9
t^2 ≈ 4.082
t ≈ √4.082
t ≈ 2.02 seconds (approx.)
For the second stone:
h2 = u2t + (1/2)gt^2
5 = 0*t + (1/2)*9.8*t^2
5 = (4.9t^2)
t^2 = 5/4.9
t^2 ≈ 1.02
t ≈ √1.02
t ≈ 1.01 seconds (approx.)
The time interval between the two stones hitting the ground is the difference between the times it takes for each stone to hit the ground.
Time interval = t1 - t2 = 2.02 seconds - 1.01 seconds = 1.01 seconds
Therefore, the time interval between the two stones hitting the ground is approximately 1.01 seconds.