To determine the maximum height reached by the volleyball, we can analyze its vertical motion.
The vertical motion of the ball can be described using the following equations:
- Vertical displacement (Δy) = (Initial velocity * sin(θ))^2 / (2 * acceleration due to gravity)
- Final velocity in the vertical direction (v_y) = Initial velocity * sin(θ) - (acceleration due to gravity * time)
where:
- Initial velocity is the magnitude of the initial velocity (5 m/s).
- θ is the launch angle (35 degrees).
- acceleration due to gravity is the acceleration experienced by the ball (approximately 9.8 m/s^2).
- time is the total time taken for the ball to reach the maximum height and then return to the ground.
First, let's find the time taken for the ball to reach the maximum height. Since the ball reaches the same height on its way up and down, the total time can be calculated as twice the time taken for the ball to reach its highest point.
Using the equation v_y = Initial velocity * sin(θ) - (acceleration due to gravity * time), we can solve for time:
0 = (5 * sin(35)) - (9.8 * time)
Solving for time:
9.8 * time = 5 * sin(35) time = (5 * sin(35)) / 9.8
Now we can calculate the maximum height by substituting this time value into the first equation:
Δy = (5 * sin(35))^2 / (2 * 9.8)
Calculating further:
Δy ≈ (5 * 0.574)^2 / (2 * 9.8) ≈ 1.327 / 19.6 ≈ 0.0676 meters
Therefore, the maximum height reached by the volleyball, when air resistance is ignored, is approximately 0.0676 meters.