To find the maximum height reached by a stone thrown up at an angle of 60 degrees with an initial velocity of 30 meters per second, we can use the equations of projectile motion.
The initial vertical velocity (Vy) can be calculated as Vy = V * sin(θ), where V is the initial velocity and θ is the angle of projection.
Given: V = 30 m/s (initial velocity) θ = 60 degrees (angle of projection)
Vy = 30 * sin(60) Vy = 30 * (√3 / 2) Vy = 15√3 m/s
The maximum height (H) can be found using the equation:
H = (Vy^2) / (2g)
where g is the acceleration due to gravity, which is approximately 9.8 m/s².
H = (15√3)^2 / (2 * 9.8) H = (225 * 3) / 19.6 H = 675 / 19.6 H ≈ 34.43 meters
Therefore, the maximum height reached by the stone is approximately 34.43 meters.