a stone is projected at an angle 60 degree and an initial velocity of 20m/s. determine the time of flight
Fomular for a stone is projected as an angle of 60% and initial velocity of 20m/s determine
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Well I think the answer is calculated like this we are looking for our time (t) so therefore t=20(sin60°) and sin60 is =0.866 so 20 × 0.866 will give you 17.3secs
To determine the time of flight of a stone projected at an angle of 60 degrees and an initial velocity of 20 m/s, you can use the kinematic equations of motion for projectile motion.
The time of flight refers to the total time it takes for the stone to reach the same vertical height from which it was initially projected. In projectile motion, the vertical motion is independent of the horizontal motion.
Here's how you can find the time of flight:
1. Split the initial velocity into its horizontal and vertical components.
- The horizontal component is given by Vx = V * cos(theta), where V is the initial velocity (20 m/s) and theta is the launch angle (60 degrees).
- The vertical component is given by Vy = V * sin(theta), where V is the initial velocity (20 m/s) and theta is the launch angle (60 degrees).
2. Determine the time it takes for the stone to reach its maximum height by using the vertical component of velocity.
- At the highest point, the vertical component of velocity becomes zero (Vy = 0).
- Use the equation Vy = Vy0 + gt, where Vy0 is the initial vertical component of velocity (Vy0 = V * sin(theta)), g is the acceleration due to gravity (9.8 m/s^2), and t is the time taken.
- Rearrange the equation to solve for t: t = -Vy0 / g.
3. Multiply the time it takes to reach the maximum height by 2 to get the total time of flight.
- Since the motion is symmetrical, the time taken to reach the highest point is the same as the time taken to descend back to the initial height.
- Therefore, the total time of flight (T) is given by T = 2 * t.
Substituting the values into the equations:
Vx = 20 m/s * cos(60 degrees) = 10 m/s
Vy0 = 20 m/s * sin(60 degrees) = 17.321 m/s
t = (-17.321 m/s) / (-9.8 m/s^2) ≈ 1.768 s
T = 2 * t ≈ 2 * 1.768 s ≈ 3.536 s
Therefore, the time of flight of the stone is approximately 3.536 seconds.
the stone's upward velocity is
v = 20 sin60° - 9.8t
how long does it take to stop rising? That's ha;f the total flight time.