a stone is projected upwards at an angle of 30 degree to the horizontal from the top of a tower 100m and it hits the ground at a point Q. If the initial velocity of projection is 100m/s2.calculate the maximum height of the stone above the ground
To calculate the maximum height of the stone, we can use the equations of motion under projectile motion.
First, let's split the initial velocity into its horizontal and vertical components. The initial velocity (100 m/s) can be represented as 2 vectors - one along the horizontal direction and the other along the vertical direction. Since the angle of projection is 30 degrees to the horizontal, we can find the components using trigonometry.
The horizontal component, Vx, can be calculated as:
Vx = V * cos(theta)
Vx = 100 m/s * cos(30 degrees)
Vx = 100 m/s * √3/2
Vx = 50√3 m/s
The vertical component, Vy, can be calculated as:
Vy = V * sin(theta)
Vy = 100 m/s * sin(30 degrees)
Vy = 100 m/s * 1/2
Vy = 50 m/s
Now let's analyze the vertical motion of the stone. The initial vertical velocity is 50 m/s, and the acceleration is the acceleration due to gravity, which is approximately -9.8 m/s² (negative due to being directed downwards). We want to find the maximum height, so the final vertical velocity at the topmost point will be zero.
We can use the equation of motion to find the time it takes for the stone to reach its maximum height:
Vy = Uy + a * t
0 = 50 m/s + (-9.8 m/s²) * t
Solving for t, we get:
9.8 m/s² * t = 50 m/s
t ≈ 5.10 seconds
Now, we can use this time to calculate the maximum height using the equation of motion:
s = Ut + 1/2 * a * t²
s = 50 m/s * 5.10 seconds + 1/2 * (-9.8 m/s²) * (5.10 seconds)²
s ≈ 255 meters
Therefore, the maximum height of the stone above the ground is approximately 255 meters.