00:01
Hi, in this question we have a stone is dropped from a building which is 256 feet high.
00:07
So we have this to 56 feet.
00:13
We want to find the equation of the motion of the stone.
00:15
So let's write out the knowns.
00:18
So we know the acceleration of its gravity, which is equal to 9 .8, 1 meters per second squared.
00:25
We also know the vertical distance which is called our y.
00:29
And we need to convert this to meters so why in meters would be equal to approximately 78 meters so for the equation of the motion of the stone we want to find an equation that represent the position of the stone at every time in this motion so we have finished the equation y is equal to v0 t plus half a t squared so y is going to be that vertical displacement at a pascalate time so let's call this yt y t so y at a particular time it's equal to v not which is the initial velocity in the vertical direction and that is going to be called to zero because this drop from rest which is going to be half the acceleration is going to be the acceleration of gravity times 9 .8 1 t squared simplifying this you have yt is equal to 4 .9 t squared so that's our equation for the motion the position of the stone at general equation for the position of the stone so for next next one to find the instantaneous velocity of the stone at one second two seconds at one and two seconds so we have the equation v is equal to v knot plus a t where v knot is nigh -velocity as before is the acceleration which will be the acceleration just gravity t is the time so v is equal to 0 plus 9 .81.
02:14
Now first for time of 1, called us v1, representing the time of 1 times 1.
02:29
And v1 will be equal to 9 .8 1, mute that per second.
02:37
Next, v2, time at 2 seconds, would be called to 0 plus 9 .81 times 2, 2 to be called 2 to be called 2, 2 19 .6 meters per second.
02:57
Next one to find the time it takes for the stone to raise the ground...