Understanding the Motion:
* Upward Journey: When a body is projected upwards, it initially has a positive velocity. As it moves against gravity, the velocity decreases until it reaches zero at the highest point. Then, it starts falling back down.
* Downward Journey: On the way down, the velocity increases in the negative direction (downwards) until it reaches the ground.
Key Equations:
We'll use the following equations of motion:
* v = u + at: where:
* v = final velocity
* u = initial velocity
* a = acceleration (due to gravity, g = -9.8 m/s²)
* t = time
* s = ut + (1/2)at²: where:
* s = displacement (height in this case)
Steps to Find the Heights:
1. Initial Conditions:
* Determine the initial velocity (u) of the body.
* Note that the acceleration due to gravity (a) is always -9.8 m/s².
2. Finding the Maximum Height:
* At the maximum height (H), the final velocity (v) is 0.
* Use the equation v² = u² + 2as to solve for H (displacement):
* 0² = u² + 2(-9.8)H
* H = u² / (2 * 9.8)
3. Finding the Height at a Specific Time:
* Choose a specific time (t) during the flight.
* Use the equation s = ut + (1/2)at² to solve for the height (s) at that time.
Example:
Let's say a body is projected upwards with an initial velocity of 20 m/s.
1. Maximum Height (H):
* 0² = 20² + 2(-9.8)H
* H = 20.41 meters (approximately)
2. Height at Time t = 1 second:
* s = (20)(1) + (1/2)(-9.8)(1)²
* s = 15.1 meters (approximately)
Important Notes:
* You can use the same equations to find the height at any time during the flight.
* Remember to pay attention to the direction of motion and the signs of velocity and acceleration.
* You can also use other kinematic equations, such as v = u + at, to analyze the motion in more detail.
Let me know if you have any specific scenarios you'd like to work through.
