a stone is thrown vertically upwards from the edge of a tower with velocity 5m/s.it strikes the ground close to the base after 4s .the height of tower?
To find the height of the tower, we can use the equation of motion for an object thrown vertically upwards:
h = ut + (1/2)gt²
Where:
h = height of the tower
u = initial velocity of the stone (5 m/s, upwards)
g = acceleration due to gravity (9.8 m/s², downwards)
t = time taken for the stone to strike the ground (4 s)
Using the given values, we can calculate the height of the tower as follows:
h = (5 * 4) + (1/2)(-9.8)(4)²
h = 20 - 78.4
h = -58.4 meters
The negative sign in the result indicates that the initial assumption of the direction of velocity is incorrect. The stone actually falls downwards with an initial velocity of 5 m/s. So, the height of the tower is 58.4 meters.
To find the height of the tower, we need to find the maximum height reached by the stone during its vertical motion.
We can use the following equation to find the maximum height:
h = u^2 / (2g)
Where:
h = maximum height
u = initial velocity (thrown upwards) = +5 m/s (positive because it is upwards)
g = acceleration due to gravity = -9.8 m/s^2 (negative because it is directed downwards)
Plugging in the values into the equation, we get:
h = (5 m/s)^2 / (2 * -9.8 m/s^2)
h = 25 m^2/s^2 / -19.6 m/s^2
h ≈ -1.28 m
Here, the negative sign indicates that the stone went down by 1.28 meters from its original position.
To find the height of the tower, we need to add the maximum height to the final position of the stone when it hits the ground.
Since it took 4 seconds for the stone to hit the ground, and we know that the acceleration due to gravity is -9.8 m/s^2, we can use the following equation to find the final position:
s = ut + (1/2)gt^2
Where:
s = final position
u = initial velocity = +5 m/s (positive because it is upwards)
t = time taken = 4 s
g = acceleration due to gravity = -9.8 m/s^2 (negative because it is directed downwards)
Plugging in the values, we get:
s = (5 m/s) * (4 s) + (1/2) * (-9.8 m/s^2) * (4 s)^2
s = 20 m + (-78.4 m)
s ≈ -58.4 m
Again, the negative sign indicates that the stone was below the starting position at the end.
Now, let's find the height of the tower by adding the maximum height to the final position:
Height of tower = max height + final position
Height of tower = (-1.28 m) + (-58.4 m)
Height of tower ≈ -59.68 m
Since height cannot be negative, we take the magnitude of the height:
Height of tower ≈ 59.68 m
Therefore, the height of the tower is approximately 59.68 meters.
hf=hi+vo*t-1/2 g t^2
0=hi+5*4-4.8*16
solve for hi