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. How high is this point?

Verified step by step guidance

1. Identify the vertical motion of the football. The initial upward velocity component is given as 12.0 m/s. This is the initial velocity in the vertical direction.
2. Use the kinematic equation for vertical motion to find the maximum height. The equation is: $v_f=v_i+at$, where $v_f$ is the final velocity (0 m/s at the peak), $v_i$ is the initial velocity (12.0 m/s), $a$ is the acceleration due to gravity (-9.8 m/s²), and $t$ is the time to reach the peak.
3. Solve for the time $t$ it takes to reach the peak using the equation: $t=\frac{-v_i}{a}$. Substitute the values to find $t$.
4. Use the kinematic equation for displacement to find the maximum height: $h=v_{i}t+\frac{1}{2}a{t}^2$. Substitute the values of $v_i$, $t$, and $a$ to find $h$.
5. Interpret the result: The calculated height is the maximum height reached by the football during its flight, considering only the vertical motion and ignoring air resistance.

Key Concepts

Projectile Motion

Projectile motion refers to the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. It involves two components of motion: horizontal and vertical. The horizontal motion is constant, while the vertical motion is influenced by gravity, causing the object to follow a parabolic trajectory.

Kinematic Equations

Kinematic equations describe the motion of objects in terms of displacement, velocity, acceleration, and time. For vertical motion under gravity, the equation h = v_i*t + 0.5*a*t^2 can be used, where h is the height, v_i is the initial vertical velocity, a is the acceleration due to gravity, and t is the time. These equations help calculate the maximum height reached by the projectile.

Vertical Motion under Gravity

Vertical motion under gravity is characterized by a constant acceleration downwards, typically 9.8 m/s² on Earth. When an object is projected upwards, it will decelerate until it reaches its peak height, where the vertical velocity becomes zero. Understanding this concept is crucial for determining the maximum height of a projectile.