A physics student on Planet Exidor throws a ball, and it follows the parabolic trajectory shown in FIGURE EX4.13. The ball's position is shown at 1 s intervals until t = 3s. At t = 1s, the ball's velocity is v = (2.0 i + 2.0 j) m/s. (b) What is the value of g on Planet Exidor?

Verified step by step guidance

1. Identify the components of the velocity vector at t = 1s. The velocity vector is given as v = (2.0 i + 2.0 j) m/s, where 'i' represents the horizontal component and 'j' represents the vertical component.
2. Recognize that the vertical component of the velocity vector (2.0 j m/s) will be influenced by the planet's gravitational acceleration, g. The horizontal component (2.0 i m/s) remains constant as gravity only affects vertical motion.
3. Understand that the vertical velocity changes due to gravity. The formula for the change in vertical velocity is given by v_f = v_i + g*t, where v_f is the final vertical velocity, v_i is the initial vertical velocity, and t is the time elapsed.
4. Determine the change in vertical velocity between two time intervals (e.g., from t = 1s to t = 2s) using the position or velocity data provided for those times. This change is due to the gravitational acceleration.
5. Solve for g using the equation derived from the change in vertical velocity. Rearrange the formula to isolate g: g = (v_f - v_i) / t.

Key Concepts

Projectile Motion

Projectile motion refers to the motion of an object that is thrown or projected into the air, subject to the force of gravity. It follows a curved path known as a parabola, characterized by horizontal and vertical components of motion. The horizontal motion is uniform, while the vertical motion is influenced by gravitational acceleration, leading to a change in velocity over time.

Acceleration due to Gravity (g)

The acceleration due to gravity, denoted as 'g', is the rate at which an object accelerates towards the center of a planet due to gravitational force. On Earth, this value is approximately 9.81 m/s², but it can vary on different planets. In the context of projectile motion, 'g' affects the vertical component of the object's velocity and determines the shape and duration of its trajectory.

Velocity Components

Velocity components refer to the breakdown of an object's velocity into its horizontal and vertical parts. In the given problem, the ball's velocity at t = 1s is expressed as v = (2.0 i + 2.0 j) m/s, where 'i' represents the horizontal component and 'j' the vertical component. Understanding these components is crucial for analyzing the motion and calculating the effects of gravity on the ball's trajectory.