A rookie quarterback throws a football with an initial upward velocity component of 12.0 m/s and a horizontal velocity component of 20.0 m/s. Ignore air resistance. (b) How high is this point?

Verified step by step guidance

1. Identify the initial vertical velocity component (Vy) which is given as 12.0 m/s.
2. Use the kinematic equation for vertical motion to find the maximum height. The equation is Vy^2 = 2gH, where Vy is the initial vertical velocity, g is the acceleration due to gravity (approximately 9.8 m/s^2), and H is the maximum height.
3. Rearrange the equation to solve for H: H = Vy^2 / (2g).
4. Substitute the values of Vy and g into the equation to find H.
5. Calculate H using the values Vy = 12.0 m/s and g = 9.8 m/s^2 to find the maximum height the football reaches.

Key Concepts

Projectile Motion

Projectile motion refers to the motion of an object that is launched into the air and is subject to gravitational forces. It can be analyzed in two dimensions: horizontal and vertical. The horizontal motion is uniform, while the vertical motion is influenced by gravity, leading to a parabolic trajectory. Understanding this concept is essential for solving problems involving objects thrown at an angle.

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration, such as gravity. For vertical motion, the key equation is h = v_i * t + 0.5 * a * t^2, where h is height, v_i is the initial vertical velocity, a is acceleration (gravity), and t is time. These equations allow us to calculate various parameters of motion, including maximum height and time of flight.

Components of Velocity

Velocity can be broken down into horizontal and vertical components, which are crucial for analyzing projectile motion. The initial velocity of the football is given as two components: an upward (vertical) component of 12.0 m/s and a horizontal component of 20.0 m/s. By separating these components, we can independently analyze the vertical motion to determine the maximum height reached by the projectile.