a stone is thrown vertically upward with an initial velocity u from the top of tower, reaches the ground with a velocity 3u. what is the height of tower?
final KE=initialPE-initial KE
1/2 m v^2=mgh-1/2 m u^2
1/2m(9u^2-u^2)=mgh
solve for h.
To find the height of the tower, we need to first determine the time it takes for the stone to reach the ground.
We can use the equation of motion for the vertical direction:
v^2 = u^2 + 2as
Where:
v = final velocity (3u)
u = initial velocity (u)
a = acceleration (gravity, g)
s = displacement (height of the tower, h)
Using the equation, we can solve for s:
(3u)^2 = u^2 + 2gh
Simplifying the equation:
9u^2 = u^2 + 2gh
Rearranging the equation:
8u^2 = 2gh
Now, we can solve for h:
h = 4u^2 / g
The height of the tower is given by h = 4u^2 / g.
To find the height of the tower, we can use the equations of motion for vertical motion.
Let's assume that the tower's height is represented by 'h', the initial upward velocity of the stone is 'u', and the final downward velocity of the stone when it reaches the ground is '3u'.
The equations of motion for vertical motion are:
1. Final velocity equation: v = u + at
2. Displacement equation: h = ut + (1/2)at^2
In this case, the stone is thrown vertically upward, so the acceleration due to gravity (a) acts in the opposite direction. Therefore, the value of 'a' will be negative (-9.8 m/s^2, assuming standard gravity).
Now, using the final velocity equation, we have:
3u = u - 9.8t
Simplifying this equation, we get:
3u + 9.8t = u (taking 'u' to the left-hand side and 't' to the right-hand side)
t = 2u / 9.8 (dividing both sides by 9.8)
Next, substitute this value of 't' into the displacement equation:
h = u*(2u/9.8) + (1/2)(-9.8)(2u/9.8)^2
Simplifying further:
h = 2u^2/9.8 - 2u^2/(2*9.8)
h = 2u^2/9.8 - u^2/9.8
h = u^2/9.8
Therefore, the height of the tower is h = u^2/9.8.