A player throws a ball upwards with an initial speed of 29.4 m s^-1. (a) What is the direction

step 1 In this question we're given a player is throwing a ball in the upper direction with an initial

A player throws a ball upwards with an initial speed of 29.4...

A player throws a ball upwards with an initial speed of $29.4 \mathrm{~m} \mathrm{~s}^{-1}$. (a) What is the direction of acceleration during the upward motion of the ball? (b) What are the velocity and acceleration of the ball at the highest point of its motion? (c) Choose the $x=0 \mathrm{~m}$ and $t=0 \mathrm{~s}$ to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of $x$ -axis, and give the signs of position, velocity and acceleration of the ball during its upward, and downward motion. (d) To what height does the ball rise and after how long does the ball return to the player's hands ? (Take $g=9.8 \mathrm{~m} \mathrm{~s}^{-2}$ and neglect air resistance).

A player throws a ball upwards with an initial speed of $29.4 \mathrm{~m} \mathrm{~s}^{-1}$.
(a) What is the direction of acceleration during the upward motion of the ball?
(b) What are the velocity and acceleration of the ball at the highest point of its motion?
(c) Choose the $x=0 \mathrm{~m}$ and $t=0 \mathrm{~s}$ to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of $x$ -axis, and give the signs of position, velocity and acceleration of the ball during its upward, and downward motion.
(d) To what height does the ball rise and after how long does the ball return to the player's hands ? (Take $g=9.8 \mathrm{~m} \mathrm{~s}^{-2}$ and neglect air resistance).

Key Concepts

Gravitational Acceleration

Gravitational acceleration is a constant acceleration experienced by all objects near the surface of the Earth due to the planet's gravity. It acts in the downward direction irrespective of the object's motion and is typically approximated as 9.8 m/s². This constant acceleration plays a critical role in analyzing the motion of projectiles such as a ball thrown upwards.

Kinematic Equations for Uniform Acceleration

The kinematic equations govern the motion of objects under constant acceleration and relate displacement, initial velocity, time, and acceleration. They allow us to calculate various parameters of the motion, such as the maximum height reached by a projectile and the time taken for its complete motion, by incorporating the effects of gravitational acceleration.

Velocity at Maximum Height

At the highest point of its trajectory, a projectile's upward velocity becomes zero momentarily before it begins to fall back down due to gravitational pull. Despite the change in velocity, gravitational acceleration remains constant, ensuring that the acceleration at the peak is still directed downward.

Coordinate System and Sign Conventions

Selecting an appropriate coordinate system and defining sign conventions is essential for analyzing projectile motion. For example, choosing a reference point as the origin and specifying which direction is positive allows for consistent treatment of vector quantities such as displacement, velocity, and acceleration. The assignment of signs to these quantities affects the equations and physical interpretation of the motion, especially when analyzing different phases like upward and downward motion.

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