A stone projected at an angle of 60 degree and intial velocity of 20 meter second determing the time of flight

THE ANSWER IS 3.46s

To determine the time of flight of a stone projected at an angle of 60 degrees with an initial velocity of 20 meters per second, we can use some basic principles of projectile motion.

The motion of the stone can be divided into two components: horizontal and vertical. The horizontal component remains constant throughout the motion, while the vertical component is affected by gravity.

First, let's find the time taken for the stone to reach its maximum height. At the highest point, the vertical component of the velocity becomes zero. We can use the following formula to find the time taken to reach the maximum height:

t = (V * sin θ) / g

where:
t = time of flight
V = initial velocity = 20 m/s
θ = angle of projection = 60 degrees
g = acceleration due to gravity = 9.8 m/s^2

Substituting the given values into the formula:

t = (20 * sin 60) / 9.8

Using the value of sin 60 (which is √3 / 2) and simplifying the equation:

t = (20 * √3 / 2) / 9.8
t = (10√3 / 9.8)

Now, we need to find the total time of flight. Since the stone will take the same amount of time to reach its maximum height and return to the ground, we can multiply the time taken to reach the maximum height by 2:

Total time of flight = 2 * t
Total time of flight = 2 * (10√3 / 9.8)

Thus, the time of flight for the stone projected at an angle of 60 degrees with an initial velocity of 20 meters per second is (20√3 / 9.8) seconds, or approximately 2.04 seconds.