The problem in the image involves a player shooting a ball at an initial velocity of 20 m/s at an angle of 60 degrees above the horizontal. We are asked to:

• (a) Determine the approximate range of the ball.
• (b) Calculate the maximum height of the ball.
• (c) Find the time it takes for the ball to reach point B from point A (half of the trajectory).
• (d) Find the total time the ball is in motion from point A to point B.

To solve this, we use the following kinematic equations for projectile motion:

• Horizontal and vertical components of velocity: $v_{x} = v_0 \cdot \cos(\theta)$ $v_{y} = v_0 \cdot \sin(\theta)$ where $v_0$ is the initial speed (20 m/s), and $\theta$ is the angle (60 degrees).

• Range: The range $R$ is the horizontal distance the ball travels before hitting the ground: $R = \frac{v_0^2 \cdot \sin(2\theta)}{g}$ where $g$ is the acceleration due to gravity (9.8 m/s²).

• Maximum height: The maximum height $H$ is reached when the vertical component of the velocity becomes zero: $H = \frac{v_0^2 \cdot \sin^2(\theta)}{2g}$

• Time to reach maximum height: The time to reach the highest point (half of the total time) is given by: $t_{\text{half}} = \frac{v_0 \cdot \sin(\theta)}{g}$

• Total flight time: The total flight time is twice the time to reach the maximum height: $T = 2t_{\text{half}} = \frac{2v_0 \cdot \sin(\theta)}{g}$

Let me compute these values for each part.Here are the results for the projectile motion problem:

• (a) The approximate range of the ball is 35.35 meters.
• (b) The maximum height of the ball is 15.31 meters.
• (c) The time it takes for the ball to reach point B (the highest point) is 1.77 seconds.
• (d) The total flight time for the ball from point A to point B (when it hits the ground again) is 3.53 seconds.

Would you like more details on the calculations or any of the steps?

Here are five related questions for further exploration:

1. How would changing the angle of projection affect the range of the ball?
2. What would the range be if the initial velocity were increased to 30 m/s?
3. How does air resistance impact the calculations in real-world conditions?
4. Can you calculate the ball's velocity at different points during its flight?
5. How would you calculate the distance at any given time, $t$, during the flight?

Tip: For maximum range in projectile motion, the ideal launch angle is 45 degrees when air resistance is neglected.