Unit 1 Topic 1.2: Motion in 2D and 3D

What are Scalars?

Quantities fully described by a magnitude, e.g., mass, time, temperature.

What are Vectors?

Quantities described by both a magnitude and a direction, e.g., displacement, velocity, force.

What do unit vectors represent?

Vectors with a magnitude of 1 pointing in the direction of the coordinate axes.

How do you represent a generic vector A?

As A = Axi + Ayj + Azk.

What is the formula to find the magnitude of a vector?

|A| = sqrt(Ax² + Ay²) in 2D.

How do you determine the direction of a vector?

By using θ = tan⁻¹(Ay/Ax).

What does constant velocity imply in projectile motion?

Horizontal motion (x-axis) has no acceleration (ax = 0) and velocity is constant.

What is the acceleration in vertical motion for projectile motion?

a_y = -g, where g is approximately 9.8 m/s².

What are the equations of motion for vertical motion in projectiles?

vy(t) = v0y - gt and y(t) = y0 + v0yt - (1/2)gt².

What is the independence of motion principle?

The horizontal and vertical motions are independent yet linked by time.

How do you decompose initial velocity in projectile motion?

v0x = v0cos(θ) and v0y = v0sin(θ).

What does the Range Formula R = v_0²sin(2θ)/g assume?

It assumes launch height equals landing height (level ground).

What is a common misconception about vertical velocity at the peak?

v_y = 0 at the peak does not mean total velocity v = 0; horizontal velocity remains constant.

What is the formula for velocity of A relative to B?

vAB = vAC + v_CB.

How do you use the chain rule for relative motion?

You can insert an intermediate frame C: vAB = vAC - v_BC.

How is the velocity of a boat relative to ground determined if the river flows?

vBG = vBW + v_WG.

What mistake is common with mixing vector components?

Using vertical acceleration in horizontal equations or vice versa.

How should you structure calculations for projectile motion?

Create two distinct columns: one for X-data and one for Y-data.

Why must you check calculator mode settings before an exam?

To avoid errors when calculations require either degrees or radians.

What time of flight formula is used in vertical motion analysis?

0 = y0 + v0yt - (1/2)gt².

When calculating the horizontal distance traveled during projectile motion, what factors are involved?

Use horizontal velocity and time of flight.

What is the significance of knowing the frame of reference in relative motion?

It determines how the velocities of objects are perceived and measured.

What is the formula to find the speed of a boat relative to the shore?

By calculating the magnitude of 𝑣_BG from its components.

What does a negative sign in acceleration indicate?

It indicates a direction opposite to the defined positive direction, often downwards.

What should you avoid when using the Range Formula in projectile problems?

Avoid relying on it unless the trajectory starts and ends at the same height.