a projectile is fired at an angle of 60 degrees with the horizontal and with the initital velocity of 80 m/s. What is the time of flight?
t = 2•v(i) •sin(2α)/g
Sorry!
t = 2•v(i) •sin(α)/g
Elena's second answer for the time of flight is correct. The angle 2á enters when calculating the range.
In your case, á = 60 degrees
To find the time of flight of a projectile, you can use the basic principles of projectile motion.
The time of flight refers to the total time it takes for the projectile to reach its highest point and then land back on the same horizontal level from where it was initially fired.
To calculate the time of flight, you need to consider the vertical motion of the projectile. In this case, the projectile is fired at an angle of 60 degrees with the horizontal, so you'll need to split the initial velocity into its horizontal and vertical components.
The horizontal component (Vx) is given by:
Vx = V * cos(θ)
where V is the initial velocity and θ is the angle of projection.
In this case, V = 80 m/s and θ = 60 degrees, so:
Vx = 80 * cos(60)
Now, we can determine the time of flight by considering the vertical motion of the projectile. The time it takes for the projectile to reach its highest point and then land on the same horizontal level is equal to twice the time it takes for the projectile to reach its highest point.
The vertical component (Vy) is given by:
Vy = V * sin(θ)
where V is the initial velocity and θ is the angle of projection.
In this case, V = 80 m/s and θ = 60 degrees, so:
Vy = 80 * sin(60)
Since the time taken to reach the maximum height is the same as the time taken to descend back down to the same level, you can use the vertical component (Vy) to find the time taken for either phase.
The time taken to reach the maximum height can be found using the equation:
t = Vy / g
where g is the acceleration due to gravity, approximately 9.8 m/s^2.
Once you find the time taken for one phase, you can multiply it by 2 to find the total time of flight.
By following these steps, you can calculate the time of flight for the given projectile fired at an angle of 60 degrees with an initial velocity of 80 m/s.