A physics problem?

Question

A roof tile falls from rest from the top of a building. An observer inside the building notices that it takes 0.24 s for the tile to pass her window, whose height is 2.5 m. How far above the top of this window is the roof? Answer in meters

Answer 1

You can use the formula d = vi * t + (a * t^2) / 2 to find out its initial velocity, then find out what distance it must have travelled to gain that velocity.

distance traveled = 2.5 m
time elapsed = 0.24 s
2.5 = vi * .24 + (9.8 * [.24]^2)) / 2
2.5 = vi * .24 + .28224
(2.5 - 0.28244) / .24 = vi
9.24066 = initial velocity (Velocity when it passed the window)
v / t = a
9.24066 / t = 9.8
9.24066 / 9.8 = t
.9429 = t

now to find out how far it travelled:
d = vi * t + (a * t^2) / 2
d = 0t + (9.8 * .9429^2) / 2
d = 4.35m

lol walked away and went to work without hitting SUBMIT.

Answer 2

Good Question. Here we go:
Let us assume that the velocity of the tile when it is at the top of the window be u m/s.

Then s = u*t + 1/2*g*t^2
Here s = 2.5m, t = 0.24 s and g = 9.81m/s^2. We need to find out u.

2.5 = 0.24*u + 1/2*9.81*0.24^2
2.5 = 0.24*u + 0.282528
u = 9.24 m/s

Now this is the velocity with which the roof tile reaches the top of the window.
Initially the velocity of the tile before it falls is zero. Let the height of this point from the point at which it reaches the velocity of 9.24m/s be h. Since acceleration is due to gravity, therefore using V^2 - U^2 = 2*g*h......U = 0 & V = u = 9.24 m/s
9.24^2 = 2*9.81*h
h = 4.35 m

Hence the top of the window is 4.35m away from the roof.

Answer 3

This is pretty easy, but takes some reasoning.

Assuming no air resistance, and not worrying about height vs. gravity variance, you have acceleration at 9.8 m/s down. Meaning for the first second, it's ave. vel. is 9.8, second two is 17.6, etc.

Since we know how much time it took to go a certain distance in the direction of the acceleration we can calculate it's average speed for passing the window.

2.5m/.24s =x m/1s

Cross multiply and solve for x.

You have an ave speed of 10.416m/s.

So how long has it been falling?

More than a second, right?

Ave vel for 1st sec 9.8
10.416-9.8=.616

So we need to allow for that extra .616

Ave speed of the 2nd second is 2*9.8.
.616/(2*9.8)

So the acceleration increased its speed that extra .616 in half the time of the first second.

So it's been traveling for 1.308 seconds

It travelled 9.8 meters the 1st second and would have travelled an aditional 17.6 meters in the second, but it only travelled .308 seconds.
17.6*.308=5.4208
so add 9.8

15.2208

And you have the distance from the middle of the window to the roof.

Subtract out half the height of the roof (1.25m) and you have 13.9708 meters from the top of the window to the roof.

i think. =)

Answer 4

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