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Quiz: Motion in Two Dimensions

Test your understanding of two-dimensional motion, projectile motion, and relative velocity.

1. What is the fundamental principle that allows us to analyze two-dimensional motion?

  1. Horizontal and vertical motions are dependent on each other
  2. Horizontal and vertical motions are independent and can be analyzed separately
  3. Only the vertical motion needs to be considered
  4. Time must be different for horizontal and vertical components
Show Answer

The correct answer is B. The independence of horizontal and vertical motions is the key principle for analyzing two-dimensional motion. Each dimension can be treated separately using kinematic equations, with time as the common variable linking them. The horizontal motion doesn't affect the vertical motion and vice versa. This principle dramatically simplifies complex two-dimensional problems by breaking them into two one-dimensional problems.

Concept Tested: Projectile Motion

See: Kinematic Equations in Two Dimensions

2. For an object in free fall near Earth's surface (with positive upward), what is the acceleration in the vertical direction?

  1. +9.8 m/s²
  2. -9.8 m/s²
  3. 0 m/s²
  4. Variable, depending on the object's mass
Show Answer

The correct answer is B. With the standard convention of positive upward, gravity causes a downward acceleration of -9.8 m/s². This acceleration is constant and independent of the object's mass—all objects fall at the same rate in the absence of air resistance. The negative sign indicates the direction (downward), not a decrease in speed.

Concept Tested: Free Fall

See: Free Fall

3. What is the horizontal acceleration of a projectile in flight (ignoring air resistance)?

  1. 9.8 m/s² downward
  2. 9.8 m/s² horizontal
  3. Zero
  4. It depends on the launch angle
Show Answer

The correct answer is C. In projectile motion with no air resistance, there are no horizontal forces acting on the object, so the horizontal acceleration is zero. This means the horizontal velocity remains constant throughout the flight. Only gravity acts on the projectile, affecting only the vertical motion. The launch angle affects the initial velocity components but not the acceleration.

Concept Tested: Projectile Motion

See: Projectile Motion

4. A ball is thrown horizontally from a cliff. Compared to dropping it straight down, the horizontal throw will result in the ball hitting the ground:

  1. Sooner
  2. Later
  3. At the same time
  4. It depends on how hard it was thrown
Show Answer

The correct answer is C. Both balls hit the ground at the same time because their vertical motions are identical—both start with zero vertical velocity and experience the same downward acceleration due to gravity. The horizontal velocity doesn't affect the vertical motion. This demonstrates the independence of horizontal and vertical components in projectile motion. The horizontally thrown ball travels farther horizontally, but the time in the air is determined solely by vertical motion.

Concept Tested: Horizontal Projection

See: Horizontal Projection

5. For a projectile launched at an angle, at what point in its trajectory is the vertical velocity zero?

  1. At launch
  2. At the highest point
  3. At landing
  4. The vertical velocity is never zero
Show Answer

The correct answer is B. At the highest point of the trajectory, the vertical velocity is momentarily zero as the projectile transitions from moving upward to moving downward. However, the horizontal velocity remains constant throughout, and the acceleration is still -9.8 m/s² (gravity never stops acting). This is the turning point where v_y changes from positive to negative.

Concept Tested: Angled Projection

See: Angled Projection

6. A projectile is launched at 20 m/s at an angle of 30° above the horizontal. What is the initial horizontal velocity component?

  1. 10 m/s
  2. 17.3 m/s
  3. 20 m/s
  4. 34.6 m/s
Show Answer

The correct answer is B. The horizontal component is calculated using v_x = v₀ cos(θ) = 20 cos(30°) = 20 × 0.866 = 17.3 m/s. The cosine function gives the adjacent side (horizontal component) of the velocity triangle. This component remains constant throughout the projectile's flight since there's no horizontal acceleration.

Concept Tested: Angled Projection

See: Kinematic Equations in Two Dimensions

7. Two people are on a train moving at 15 m/s east. Person A walks toward the back of the train at 2 m/s relative to the train. What is Person A's velocity relative to the ground?

  1. 2 m/s west
  2. 13 m/s east
  3. 15 m/s east
  4. 17 m/s east
Show Answer

The correct answer is B. Relative velocity problems require adding vectors. The train moves 15 m/s east (positive), and Person A walks 2 m/s toward the back (west, or negative). Relative to the ground: v = 15 m/s - 2 m/s = 13 m/s east. Person A is still moving east relative to the ground, just slower than the train because they're walking backward.

Concept Tested: Relative Velocity

See: Relative Velocity

8. An object is dropped from a height of 20 meters. Using g = 10 m/s² for simplicity, how long does it take to hit the ground?

  1. 1 second
  2. 2 seconds
  3. 4 seconds
  4. 10 seconds
Show Answer

The correct answer is B. Using the kinematic equation y = y₀ + v₀t - ½gt², with y = 0 (ground), y₀ = 20 m, v₀ = 0 (dropped), and g = 10 m/s²: 0 = 20 + 0 - ½(10)t², which gives 5t² = 20, so t² = 4, and t = 2 seconds. This demonstrates free fall motion starting from rest.

Concept Tested: Free Fall

See: Free Fall

9. In projectile motion, which component of velocity changes during flight?

  1. Only the horizontal component
  2. Only the vertical component
  3. Both horizontal and vertical components
  4. Neither component changes
Show Answer

The correct answer is B. Only the vertical component of velocity changes during projectile motion because gravity acts only in the vertical direction. The vertical velocity decreases as the projectile rises (becomes less positive), reaches zero at the peak, then increases as it falls (becomes more negative). The horizontal component remains constant throughout the flight because there's no horizontal acceleration.

Concept Tested: Projectile Motion

See: Projectile Motion

10. What path does a projectile follow when launched at an angle (ignoring air resistance)?

  1. A straight line
  2. A parabola
  3. A circle
  4. An ellipse
Show Answer

The correct answer is B. The trajectory of a projectile is a parabola, which emerges from combining linear horizontal motion (x = v_x·t) with quadratic vertical motion (y = y₀ + v₀y·t - ½gt²). When you eliminate time from these equations, you get a quadratic relationship between x and y, which defines a parabolic curve. This elegant result demonstrates how simple physical principles produce beautiful mathematical patterns.

Concept Tested: Projectile Motion

See: Projectile Motion