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Hi there.
00:01
In the question, it is given that at certain instant, the stone is 10 feet above the ground and after two seconds the stone is 14 feet above the ground.
00:13
So we have to find the initial height from which the stone was dropped.
00:18
So first let us see a picture which depicts the situation.
00:23
So let h be the initial height at which the stone was dropped.
00:28
So the h will be the height from above the ground.
00:33
So a certain instant the stone reaches 110 feet and after two seconds the stone reaches 14 feet above the ground.
00:43
Okay.
00:44
So here we'll be using the equations of motion.
00:49
We can use this equation that is s is equal to ut plus half 80 square which is one of the equations of motion for solving this problem.
00:59
Here s is displacement, u is initial velocity, a is acceleration and t is the time taken.
01:06
So using this, we can find the velocity when the stone reaches 110 feet above the ground.
01:12
So here we can see that displacement s can be taken as s is equal to 110 minus 14 and that is equal to 86 feet.
01:27
Okay, so displacement is equal to 86 feet and u is something which is unknown and a can be taken as acceleration due to gravity and it is 32 feet per second square and t is equal to two seconds because it took two seconds to cover the distance of this 86 feet.
01:51
So we can say that we can just substitute all these in the given equation.
01:57
So we'll be getting s is equal to ut plus half a t square.
02:04
So while substituting it, we'll be getting 86 is equal to u multiplied by 2 plus half multiplied by 32 multiplied by t square, which is 2 square.
02:21
So we'll be getting 2 square.
02:23
This implies that 86 is equal to 2u plus 64.
02:29
So from here we'll get that.
02:33
We'll be getting that 2u is equal to 86 minus 64 and that is equal to 22 which implies u equal to 22 divided by 2 that is equal to 11 feet per second.
02:49
So the initial velocity u is equal to 11 feet per second.
02:53
So we can conclude that at the instant 1 10 feet above the ground the stone has velocity 11 feet per second.
03:01
Now we'll use another equation of motion for proceeding further.
03:08
That is v is equal to u plus a t where v is the final velocity, u is the initial velocity, a is acceleration and t is the time taken.
03:18
So this can be used to find the time taken for the stone to reach 1 10 feet above the ground from the height it was dropped.
03:29
So let's see how we'll find that.
03:31
We'll be taking v as the velocity at 1 .10 feet above the ground.
03:43
So we can say that this is equal to 11 feet per second because we have found it earlier that it is 11 feet per second...