Understanding the Physics
* Uniform Acceleration: The particle is moving under the influence of gravity, which provides a constant downward acceleration (usually denoted as 'g', approximately 9.8 m/s²).
* Initial Velocity: Let the initial velocity of the particle be 'u'.
* Final Velocity at Maximum Height: At the maximum height (H), the particle's velocity momentarily becomes zero.
Using Equations of Motion
We can use the following equation of motion to relate the height (h) to time (t):
h = ut + (1/2)gt²
Let's break down the steps:
1. Finding the Initial Velocity (u):
* Using the equation v = u + at, where 'v' is the final velocity (0 at maximum height), and 'a' is the acceleration due to gravity (-g), we get:
0 = u - gT
u = gT
2. Substituting the Initial Velocity:
* Now we can substitute the value of 'u' in the equation of motion:
h = (gT)t + (1/2)(-g)t²
h = gTt - (1/2)gt²
3. Maximum Height (H):
* The maximum height (H) is reached at time T. Substituting t = T in the above equation:
H = gT² - (1/2)gT²
H = (1/2)gT²
4. Height at Any Time (t):
* Finally, we can express the height (h) of the particle at any time 't' (0 ≤ t ≤ T):
h = gTt - (1/2)gt²
Important Notes:
* This equation only applies during the upward motion of the particle (0 ≤ t ≤ T).
* If you need to determine the height for times after the particle reaches its maximum height, you'll need to consider its downward motion.
