Motion in Two Dimensions - Projectile Motion (Notes Review)

A set of Q&A flashcards covering the key concepts and worked examples of projectile motion, including horizontal/vertical components, constant acceleration due to gravity, and how to solve common problems.

What is projectile motion?

Motion of a body moving along both horizontal and vertical axes under the influence of gravity.

What is the trajectory in projectile motion?

The path followed by the projectile.

When a projectile is thrown horizontally, what are the characteristics of its horizontal and vertical motions?

Horizontal motion is uniform (no horizontal acceleration) and vertical motion accelerates downward due to gravity; the two motions combine to form the trajectory.

At the top of an upward-angled projectile's path, what is true about its velocity?

The vertical component of velocity is zero, so the velocity is purely horizontal (and the horizontal component is constant).

How does horizontal velocity behave during the projectile’s flight?

Horizontal velocity remains constant (no horizontal acceleration). The vertical velocity changes due to gravity.

What is the acceleration acting on a projectile near Earth at all points in its flight?

A constant downward acceleration due to gravity g = 9.8 m/s^2.

What are the standard displacement equations for horizontal and vertical motion in projectile problems?

Horizontal: dx = vx t; Vertical: dy = vy0 t + (1/2) ay t^2 with ay = -g and vy = vy0 + a_y t.

In projectile motion, what are the horizontal and vertical velocity components?

vx is constant and equals the initial horizontal velocity; vy changes with time as vy = vy0 - g t.

Example 1: A body moves horizontally at 80 m/s from a cliff 50 m high. What are the time of flight and horizontal range?

Time of flight t ≈ 3.19 s; horizontal range dx ≈ 255 m.

Example 2: A cannonball with muzzle speed 1000 m/s is fired horizontally from a cliff. After 35 s, what are its vertical and horizontal displacements?

dy ≈ -6002.5 m; dx ≈ 35,000 m.

In Example 2, what are the velocity components after 35 s?

vx = 1000 m/s (constant); vy = -343 m/s; magnitude ≈ 1057 m/s; direction θ ≈ -18.93° relative to the +x axis.

Example 3: Ball kicked at 45° upward with 80 m/s from a 50 m high cliff. What are the time of flight and horizontal displacement?

Time of flight t ≈ 12.37 s; horizontal displacement dx ≈ 700.14 m.

How do you calculate vertical displacement dy when given v0y, ay, and t?

dy = v0y t + (1/2) ay t^2.

For the 45° launch example, how is the time of flight found?

Solve the vertical motion equation: -50 = v0_y t - (1/2) g t^2, leading to 4.9 t^2 - 56.57 t - 50 = 0; positive root t ≈ 12.37 s.

What is the horizontal displacement dx for the 45° launch example?

dx = v0_x t = 56.57 m/s × 12.37 s ≈ 700.14 m.

What is the Big Idea stated in the notes?

Everything that moves toward the ground undergoes projectile motion.