a stone drops from the edge of the roof. it crosses a window 2m long in 0.1sec. how much time does the stone take to reach the lower end of window from roof?
To find the time it takes for the stone to reach the lower end of the window from the roof, we need to use the information given.
First, let's calculate the speed of the stone as it crosses the window. Since the distance is 2 meters and the time is 0.1 seconds, we can divide the distance by the time:
Speed = Distance / Time
Speed = 2 meters / 0.1 seconds
Speed = 20 meters per second
Now, remember that the stone is dropped from the edge of the roof, which means it starts with an initial velocity of zero. As the stone falls, it will accelerate due to gravity. The acceleration due to gravity is approximately 9.8 meters per second squared.
We can use the equation of motion to find the time it took for the stone to reach the lower end of the window from the roof:
Final velocity = Initial velocity + (Acceleration * Time)
Since the final velocity is 20 meters per second and the initial velocity is 0, we have:
20 = 0 + (9.8 * Time)
Now we can solve this equation for Time:
20 = 9.8 * Time
Dividing both sides of the equation by 9.8 gives us:
Time = 20 / 9.8
Time ≈ 2.04 seconds
Therefore, it takes approximately 2.04 seconds for the stone to reach the lower end of the window from the roof.
average speed crossing window = 20 m/s
now look at increase of speed in 2 meter drop
v = Vi + 9.8 (2)
call g = 10 for simplicity
v = Vi + 20
but we know (v+Vi)/2 = 20 the average
v = Vi + 20
v = -Vi + 40
0 = 2 Vi -20
Vi = 10 at top of window
so how long did it fall to the top of the window?
v = g t = 10
t = 1 second from roof to top of window
so time to bottom of window = 1 + .1 = 1.1 seconds
average speed crossing window = 20 m/s
now look at increase of speed in 2 meter drop
v = Vi + 9.8 (.1)
call g = 10 for simplicity
v = Vi + 1
but we know (v+Vi)/2 = 20 the average
v = Vi + 1
v = -Vi + 40
--------------
0 = 2 Vi -39
Vi = about 20 at top of window
so how long did it fall to the top of the window?
v = g t = 20
t = 2 second from roof to top of window
so time to bottom of window = 2 + .1 = 2.1 seconds