To determine how high the ball rises, we can use projectile motion equations. Let's break down the problem step by step:
1. Identify the known values:
- Initial velocity of the ball (v₀): The ball is thrown horizontally along the track, so its horizontal component of velocity remains at 18.0 m/s.
- Initial angle with the horizontal (θ): 68.0°
- Acceleration due to gravity (g): Approximately 9.8 m/s²
2. Analyze the motion:
Since the initial velocity of the ball in the vertical direction is 0 (the ball initially rises straight up), we can use the equation: v = v₀ + gt, where v is the final vertical velocity of the ball, v₀ is the initial vertical velocity, g is the acceleration due to gravity, and t is the time.
3. Calculate the time it takes for the ball to reach its highest point:
At the highest point, the vertical velocity of the ball will be 0. Therefore, we can rearrange the equation v = v₀ + gt to solve for t: 0 = v₀ + gt.
Substituting the known values: 0 = 0 + 9.8t.
Solving for t: t = 0 s.
4. Determine the height of the ball at its highest point:
The height at the highest point can be found using the equation: h = v₀t + 0.5gt², where h is the height, v₀ is the initial vertical velocity, t is the time, and g is the acceleration due to gravity.
Substituting the known values: h = 0 + 0.5 * 9.8 * (0)².
Simplifying: h = 0.
Therefore, the ball does not rise above its initial position. It rises straight up and falls back to the same height as where it was thrown.