At a given instant the football player at A throws a...

At a given instant the football player at $A$ throws a football $C$ with a velocity of $20 \mathrm{~m} / \mathrm{s}$ in the direction shown. Determine the constant speed at which the player at $B$ must run so that he can catch the football at the same elevation at which it was thrown. Also calculate the relative velocity and relative acceleration of the football with respect to $B$ at the instant the catch is made. Player $B$ is $15 \mathrm{~m}$ away from $A$ when $A$ starts to throw the football.

Key Concepts

Projectile Motion

This concept involves analyzing the motion of an object that is launched into the air and moves under the influence of gravity only. The motion is typically decomposed into horizontal and vertical components, with the vertical motion experiencing constant acceleration due to gravity and the horizontal motion maintaining a constant velocity in the absence of air resistance.

Vector Decomposition

Vector decomposition is the process of breaking down a velocity or force vector into its horizontal and vertical components. This is crucial in problems involving projectile motion or any two-dimensional motion, as it allows the independent analysis of motion along perpendicular axes.

Kinematic Equations

Kinematic equations are a set of formulas that describe the motion of objects under constant acceleration. They relate displacement, initial velocity, final velocity, time, and acceleration. These equations are used to determine quantities like the time of flight, maximum height, and range in problems of projectile motion and linear motion.

Relative Motion Analysis

Relative motion analysis involves studying the movement of one object as observed from another moving object. This concept requires calculating relative velocity by subtracting the velocity of one object from another, and similarly, relative acceleration by subtracting their accelerations. It is an essential tool when synchronizing the motions of two bodies to meet specific conditions, such as catching a projectile at a certain location.

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