I see the math problem in the image involves analyzing the motion of a baseball through parametric equations, covering several steps:

1. Calculating horizontal and vertical velocities using derivatives of the given parametric equations.
2. Finding the speed of the baseball by combining the horizontal and vertical velocities at the point it passes over home plate.
3. Determining when the baseball hits the ground by solving for the time $t$ when the height function $y(t)$ becomes zero.
4. Calculating the angle of impact in radians, which involves finding the angle of the velocity vector at the moment the baseball hits the ground.

Here is an outline of the solutions based on the visible parts:

• Horizontal Velocity (x'(t)): It's provided directly as $144$ ft/sec.
• Vertical Velocity (y'(t)): Calculated as $-32t + 6$.
• Speed Calculation: Uses $s(t) = \sqrt{[x'(t)]^2 + [y'(t)]^2}$.
• Time to Hit Ground: Involves solving $y(t) = 0$.
• Angle of Impact: Calculated using the angle between the tangent line and the path of the ball, based on the components of velocity.

Would you like me to go through each of these steps in detail or help with a specific part? Here are five related questions to expand on these concepts:

1. How do we interpret the direction of the angle in projectile motion?
2. What would change in the calculations if air resistance was a factor?
3. How can parametric equations like these be applied to other sports or motion analysis scenarios?
4. What is the significance of converting the speed from ft/sec to mph in this context?
5. How would we solve this problem if only approximate answers were allowed?

Tip: Remember that breaking down complex motion problems into smaller parts, like analyzing horizontal and vertical components separately, simplifies solving.