Maximum height of the stone above the ground
get vetical component of velocity up at ground, call it Vi. If shot at angle A up from horizontal then Vi = V sin A
during flight acceleration = -g or 9.8 m/s^2 down or 32 ft/s^2 down
speed up = v = Vi - g t
= Vi -9.8 t or = Vi -32 t
at top, v = 0
so
t = Vi/9.8 or t = Vi/32
then h = Vi t -(9.8/2)t^2
or h = Vi t - 16 t^2
alternatively you can use conservation of energy
kinetic energy at bottom = potenial energy at top
(1/2)mVi^2 = m g h
so
Vi^2 = (2 g h)
h = Vi^2/2g
To determine the maximum height of a stone above the ground, you need to consider the factors that affect the stone's vertical motion. This can be done by applying the laws of physics, specifically the equations of motion.
Here's a step-by-step guide on how to calculate the maximum height:
1. Identify the initial conditions: Record the initial velocity (v₀) of the stone when it is launched upward and its initial height (h₀) above the ground.
2. Determine the acceleration: In most cases, the only force acting on the stone is gravity (assuming no air resistance). The acceleration due to gravity on Earth is approximately 9.8 m/s². You can assign a negative value for the acceleration since it acts in the opposite direction to the upward motion of the stone.
3. Use the kinematic equation for displacement: The equation that relates displacement (h) to initial velocity, acceleration, and time (t) is h = h₀ + v₀t + (1/2)at². However, at the maximum height, the stone reaches its peak and comes to a momentary stop, so the final velocity at the peak (v) is 0.
4. Calculate the time to reach maximum height: Since the final velocity is 0, we can substitute v = 0 into the kinematic equation. This simplifies the equation to 0 = v₀t + (1/2)at². Solve this equation for t to find the time taken to reach maximum height.
5. Substitute the calculated time into the kinematic equation: Once you know the time taken to reach the maximum height, substitute it back into the kinematic equation (h = h₀ + v₀t + (1/2)at²) to find the maximum height attained by the stone above the ground.
By following these steps, you should be able to calculate the maximum height of the stone above the ground.