a stone is projected at an angle of 60decree an and initial velocity of 20msper seconds. determine the time of the flight

I can't solve it

initial vertical velocity= 20sin60 m/s

hf=hi+20sin60*t - 4.9t^2
hf, hi are both zero, solve for time t.
This business of "I can't solve it is not much above whining". Showing some effort, or amplifying what you dont understand, or on stuck on, will lead to much better probability of success in life. Otherwise, one remains a baby.

I agree, Bobpursley.

To determine the time of flight of a stone projected at an angle of 60 degrees and an initial velocity of 20 m/s, we can use the equations of motion.

The horizontal and vertical components of the initial velocity can be calculated:

Horizontal component: Vx = V * cos(theta)
Vertical component: Vy = V * sin(theta)

Given:
Initial velocity (V) = 20 m/s
Projection angle (theta) = 60 degrees

Calculating the horizontal and vertical components:

Vx = 20 * cos(60) = 20 * 0.5 = 10 m/s
Vy = 20 * sin(60) = 20 * 0.866 = 17.32 m/s

Next, we will find the time it takes for the stone to reach its maximum height (t1) and then return to the ground (t2).

Using the equation for the vertical motion:
Vy = Vy0 + gt
where Vy = 0 (at the topmost point) and g = 9.8 m/s^2 (acceleration due to gravity).

0 = 17.32 - 9.8 * t1
t1 = 17.32 / 9.8
t1 ≈ 1.77 seconds

Since the time of flight is the sum of the time it takes to reach the maximum height and the time to return to the ground, the total time (t) is:
t = 2 * t1
t = 2 * 1.77
t ≈ 3.54 seconds

Therefore, the time of flight of the stone is approximately 3.54 seconds when projected at an angle of 60 degrees and an initial velocity of 20 m/s.