A roof tile falls from rest from the top of a building. An observer inside the building notices that it takes 0.10 s for the tile to pass her window, which has a height of 1.18 m. How far above the top of this window is the roof?
Assuming the 'passing the window'part
means 0.10s to go from the top to the bottom of the window...
Then the veocity will be 1.18/0.1, so 11.8m/s. Accel will be that of 'g', so 9.8 m/s^2; and the initial velocity was 0 m/s.
Use v^2=u^2+2as
Solve for s, which will be the height it has fallen.
what does "u" stand for?
In a scene in an action movie, a stuntman jumps from the topof one building to the top of another building 4.0m away. After arunning start, he leaps at a velocity of 5.0m/s at an angle of 15degrees with respect to the flat roof. Will he make it to the otherroof, which is 2.5m shorter than the building he jumps from?
To determine the distance above the top of the window where the roof tile fell from, we can use the equations of motion. Let's break down the problem and solve it step by step:
1. First, we need to find the time it takes for the roof tile to fall from the top of the building to the height of the window. We can use the equation of motion:
h = 0.5 * g * t^2
where,
h is the height of the window (1.18 m),
g is the acceleration due to gravity (9.8 m/s^2),
t is the time taken to pass the window (0.10 s).
Rearranging the equation to solve for time, we get:
t = sqrt(2h / g)
Substituting the given values, we have:
t = sqrt(2 * 1.18 / 9.8)
≈ 0.1542 s
So, it takes approximately 0.1542 seconds for the roof tile to fall to the height of the window.
2. Now, to find the distance above the top of the window where the roof tile fell from, we can use the equation of motion again:
h = v0 * t + 0.5 * g * t^2
where,
v0 is the initial velocity of the tile (which is zero since it falls from rest),
t is the time it takes to pass the window (0.10 s),
h is the height of the window (1.18 m).
Simplifying the equation, we have:
h = 0 + 0.5 * g * t^2
Rearranging the equation to solve for h, we get:
h = 0.5 * g * t^2
Substituting the given values, we have:
h = 0.5 * 9.8 * 0.1542^2
≈ 0.1145 m
Therefore, the roof tile fell from a distance approximately 0.1145 meters above the top of the window.