A stone is allowed to top of a tower 100m high and at the same time an...
**Solving for the Meeting Point of Two Stones**
To solve for the meeting point of the two stones, we can use the equations of motion and the concept of time of flight.
**Equations of Motion**
The equations of motion are:
`v = u + at`
`s = ut + 1/2at^2`
`v^2 = u^2 + 2as`
Where:
- `u` is the initial velocity
- `v` is the final velocity
- `a` is the acceleration
- `s` is the displacement or distance traveled
- `t` is the time taken
In this problem, we are given the initial height of one of the stones, the initial velocity of the other stone, and the acceleration due to gravity.
**Calculating Time of Flight**
We can use the equation `s = ut + 1/2at^2` to calculate the time of flight for the stone projected from the ground.
Since the stone is projected vertically upwards, the initial velocity `u` is 25 m/s and the acceleration `a` is -9.8 m/s^2 (negative because it is acting in the opposite direction of motion). The displacement `s` is 100 m (the height of the tower).
Plugging in these values, we get:
`100 = 25t + 1/2(-9.8)t^2`
Simplifying, we get a quadratic equation:
`4.9t^2 - 25t + 100 = 0`
Solving for `t` using the quadratic formula, we get:
`t = 5.1 s` or `t = 3.1 s`
Since we are only interested in the time taken for the stone to reach the top of the tower, we choose the smaller value of `t`, which is `t = 3.1 s`.
**Calculating Meeting Point**
To calculate the meeting point of the two stones, we need to find the displacement of the stone projected from the ground during the time it takes to reach the top of the tower (i.e. 3.1 s).
Using the equation `s = ut + 1/2at^2`, we get:
`s = 25(3.1) + 1/2(-9.8)(3.1)^2`
Simplifying, we get:
`s = 38.255 m`
Therefore, the meeting point of the two stones is 38.255 m above the ground.
A stone is allowed to top of a tower 100m high and at the same time an...
U1=0
U2=25m/s
h=100m
g=9.8m/S²
x=0+1/2*9.8 t²
x=4.9t² eq 1
100-x=25t-1/2 *9.8 t²
100-x=25t-4.9 t² eq 2
Adding eq 1and 2 we have
100=25t
t=100/25=4s
x=4.9*4²=78.4m
Form ground=100-78.4=21.6m
They will meet at the distane of 78.4m before the roof.
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