A projectile is fired at an angle of 60° to the vertical withe the initial velocity of 80m/s
Calculate the time of light
The. Maximum height attain
To calculate the time of flight and the maximum height attained by a projectile, we can use the equations of motion.
1. Time of flight (T):
The time of flight is the total duration the projectile is in the air. To find this, we need to calculate the time it takes for the projectile to reach its maximum height and then double that time.
Step 1: Split the initial velocity into its vertical and horizontal components.
The vertical component (Vy) is given by V * sin(θ), and the horizontal component (Vx) is given by V * cos(θ), where θ is the angle of projection and V is the magnitude of the velocity.
In this case, the initial velocity (V) is 80 m/s and the angle of projection (θ) is 60°.
Vy = 80 * sin(60°) = 69.28 m/s
Vx = 80 * cos(60°) = 40 m/s
Step 2: Calculate the time taken to reach maximum height (t1).
To calculate this, we can use the formula: t1 = Vy / g, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
t1 = 69.28 / 9.8 = 7.07 seconds (rounded to two decimal places)
Step 3: Double the time taken to reach the maximum height to get the total time of flight (T).
T = 2 * t1 = 2 * 7.07 = 14.14 seconds (rounded to two decimal places)
Therefore, the time of flight is approximately 14.14 seconds.
2. Maximum height (H):
The maximum height is the vertical distance traveled by the projectile.
Step 4: Calculate the maximum height (H).
To calculate this, we can use the formula: H = (Vy^2) / (2 * g)
H = (69.28^2) / (2 * 9.8) = 238.97 meters (rounded to two decimal places)
Therefore, the maximum height attained by the projectile is approximately 238.97 meters.
So, the time of flight is approximately 14.14 seconds, and the maximum height attained is approximately 238.97 meters.