a symmetric projectile spends a total of 20 seconds in the air. it reaches a peak height of 8 meters. how long does it take to reach its peak height? the projectile has a range of 80 meters. what is its horizontal velocity? what is the projectile's horizontal acceleration? what is the projectiles vertical acceleration?
To answer these questions, we need to understand the motion of a symmetric projectile. Let's break it down step by step:
1. How long does it take to reach the peak height?
In a symmetric trajectory, the time taken to reach the peak height is half of the total time of flight. Therefore, the projectile takes 10 seconds to reach its peak height.
2. What is the horizontal velocity?
The horizontal velocity remains constant throughout the motion of a symmetric projectile. To calculate it, we need to know the range and total time of flight. The formula to calculate the horizontal velocity is given by: Velocity = Range / Time of Flight. Given that the range is 80 meters and the total time of flight is 20 seconds, we can substitute these values into the formula to find the horizontal velocity: Velocity = 80 / 20 = 4 meters per second.
3. What is the horizontal acceleration?
Since there is no horizontal force acting on the projectile once it's launched, there is no horizontal acceleration. The horizontal velocity remains constant.
4. What is the vertical acceleration?
The vertical acceleration is caused by the force of gravity pulling the projectile downward. On Earth, the acceleration due to gravity is approximately 9.8 meters per second squared (m/s²) directed downward. Therefore, the vertical acceleration of the projectile is 9.8 m/s² downward.
To summarize:
- The projectile takes 10 seconds to reach its peak height.
- The horizontal velocity is 4 meters per second.
- The horizontal acceleration is 0 m/s² (no acceleration).
- The vertical acceleration is 9.8 m/s² downward.