Final answer:
The student can calculate the horizontal and vertical components of velocity using trigonometry and then apply projectile motion equations to find the maximum height and time to reach that height.
Step-by-step explanation:
To answer the student's question regarding a soccer ball being kicked, we'll need to decompose the ball's initial velocity into horizontal and vertical components and apply the principles of projectile motion to determine the ball's maximum height and the time it takes to reach that height.
Horizontal and Vertical Components of Initial Velocity
The horizontal component of velocity (Vx) is given by Vx = V * cos(θ), where V is the initial velocity and θ is the angle of projection.
The vertical component of velocity (Vy) is given by Vy = V * sin(θ).
Maximum Height and Time to Reach Maximum Height
The maximum height (H) can be found using the equation H = Vy^2 / (2g), where g is the acceleration due to gravity (9.81 m/s^2).
The time to reach the maximum height (t) is given by t = Vy / g.
For the given values of a 0.5-kg ball with initial velocity of 20 m/s at a 30° angle: Vx = 20 m/s * cos(30°) and Vy = 20 m/s * sin(30°). Using the given formulae, we can solve for (b) and (c).