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The image you have uploaded contains two projectile motion problems. Let’s break them down one by one:

### Problem 1: Football Kick

**Given:**
- Horizontal distance \( d = 126 \, \text{ft} \)
- Time of flight \( t = 3.6 \, \text{seconds} \)
- Determine:
  1. Initial speed \( v_0 \)
  2. Angle \( \theta \)

**Steps:**
1. **Horizontal Motion Equation**  
   The horizontal distance traveled by a projectile is given by:
   \[
   d = v_0 \cos(\theta) \cdot t
   \]
   where \( v_0 \) is the initial velocity and \( \theta \) is the angle of projection.
   - Substituting the values: 
     \[
     126 = v_0 \cos(\theta) \cdot 3.6
     \]

2. **Vertical Motion Equation**  
   The vertical displacement \( y = 0 \) (since the ball returns to the same height), and the vertical motion equation is:
   \[
   0 = v_0 \sin(\theta) \cdot t - \frac{1}{2} g t^2
   \]
   where \( g = 32.2 \, \text{ft/s}^2 \) (acceleration due to gravity).
   - Substituting values:
     \[
     0 = v_0 \sin(\theta) \cdot 3.6 - \frac{1}{2} \cdot 32.2 \cdot 3.6^2
     \]

From these two equations, we can solve for \( v_0 \) and \( \theta \).

---

### Problem 2: Basketball Shot

**Given:**
- Height of player \( A = 7 \, \text{ft} \)
- Distance between players \( A \) and \( B = 25 \, \text{ft} \)
- Player \( B \) is attempting a block at height \( h \)
- Distance from player \( B \) to the hoop is \( 5 \, \text{ft} \)
- Total height of the hoop \( = 10 \, \text{ft} \)
- Angle of projection \( \theta = 30^\circ \)

**Find:**
1. The magnitude of the initial velocity \( v_A \)
2. The height \( h \) of the ball when it passes over player \( B \)

**Steps:**
1. **Horizontal Motion Equation**  
   The horizontal motion of the ball is given by:
   \[
   d = v_A \cos(\theta) \cdot t
   \]
   where \( d = 25 \, \text{ft} \).

2. **Vertical Motion Equation**  
   The height \( y \) of the ball at a given time is:
   \[
   y = y_0 + v_A \sin(\theta) \cdot t - \frac{1}{2} g t^2
   \]
   where \( y_0 = 7 \, \text{ft} \) (initial height), and \( g = 32.2 \, \text{ft/s}^2 \).

Solving these will give the initial velocity \( v_A \) and the height \( h \) when the ball passes over player \( B \).

---

### Let me now solve both problems step-by-step.

I'll begin with the equations for the first problem to calculate the initial velocity and angle.For the first problem, the solutions are:

1. The initial velocity \( v_0 = 67.71 \, \text{ft/s} \).
2. The angle of projection \( \theta = 1.03 \, \text{radians} \) or approximately \( 59.0^\circ \).

---

Next, I'll calculate the initial velocity \( v_A \) and the height \( h \) when the basketball passes over player \( B \) in the second problem.For the second problem, the solutions are:

1. The initial velocity of the basketball \( v_A = 36.73 \, \text{ft/s} \).
2. The height of the ball when it passes over player \( B = 11.49 \, \text{ft} \).

---

Let me know if you would like further details or clarifications. Here are five additional questions for further exploration:

1. How would the results change if air resistance were taken into account?
2. What would the initial speed and angle be if the football traveled 150 ft in the same time?
3. How would the maximum height of the basketball affect the game's outcome?
4. Can you calculate the time the football spent at its maximum height?
5. What other factors influence the motion of the basketball besides velocity and angle?

**Tip:** In projectile motion, the horizontal and vertical motions are independent, except for the common time of flight.

1. From a video recording, it was observed that a professional football player kicked a football 126 feet during a measured time of 3.6 seconds. Determine the initial speed of the ball and the angle θ at which it was kicked. (from Hibbeler)

2. Measurements of a shot recorded during a basketball game are shown. The ball passed through the hoop even though it barely cleared the hands of the player B who attempted to block it. Neglecting the size of the ball, determine the magnitude vA of its initial velocity and the height h of the ball when it passes over player B. (from Hibbeler)

Learn how to solve projectile motion problems with detailed solutions for a football kick covering 126 feet in 3.6 seconds and a basketball shot. The problems include calculating the initial speed and angle of projection in a football kick and determining the initial velocity and height in a basketball shot.

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