A body is projected vertically upwards from the ground with an initial velocity of 15m\s.sketch the trajectory path of the motion
To sketch the trajectory path of the motion, you can follow these steps:
1. Understand the motion: The body is projected vertically upwards, which means it only moves along the vertical axis. The initial velocity is 15 m/s, meaning the body is moving upwards with a speed of 15 m/s.
2. Determine the key parameters: Firstly, the time it takes for the body to reach the highest point (maximum height) must be determined. Then, the time it takes for the body to fall back to the ground also needs to be calculated.
3. Calculate the times: To find the time it takes for the body to reach the maximum height, use the following equation:
\(v = u + at\)
Since the body is moving vertically upwards, the final velocity (v) becomes zero at the highest point. The initial velocity (u) is 15 m/s, and the acceleration (a) is -9.8 m/s^2 (due to gravity). Solving for time (t), we get:
\(0 = 15 - 9.8t\)
Rearranging the equation, we find:
\(t = 15 / 9.8\)
Similarly, to find the total time of flight (time for the body to reach the ground again), we can use:
\(t_total = 2t_{max}\)
Here, \(t_{max}\) is the time it takes to reach the maximum height.
4. Sketch the trajectory: Now that we have the key parameters, we can sketch the trajectory path. Start by drawing a vertical line representing the ground. Then, draw an arrow pointing upwards from the ground, indicating the direction of the initial velocity. Mark the highest point on this line, which is the maximum height. Finally, draw another arrow pointing downwards from the highest point to represent the body falling back to the ground.
Note: The actual shape of the trajectory will be a curve, but for simplicity, we can consider it as a straight line for a pure vertical projection.
By following these steps, you can sketch the trajectory path of the body projected vertically upwards.