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Sample Quiz: Physics Chapter 4

Kinematics in Two Dimensions — Physics for Scientists and Engineers: A Strategic Approach (Randall D. Knight)

10 questions · 23 points · answer key included

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Multiple Choice

  1. A ball is thrown horizontally from the top of a building at 15 m/s. At the same instant, another ball is dropped from rest from the same height. Ignoring air resistance, which statement is correct? (2 PTS)
    1. The thrown ball hits the ground first because it has initial horizontal velocity.
    2. The thrown ball takes longer to fall because its horizontal motion interferes with vertical motion.
    3. Both balls hit the ground at the same time because horizontal and vertical motions are independent.
    4. The dropped ball hits the ground first because it has no horizontal velocity to slow its fall.
  2. A spacecraft accelerates at 75 m/s2 at an angle of 25° north of east. What is the y-component (northward) of the spacecraft's acceleration? (2 PTS)
    1. 106 m/s2
    2. 68.0 m/s2
    3. 75 m/s2
    4. 31.6 m/s2
  3. A jeepney in Manila travels east at 20 m/s. A passenger on the jeepney throws a ball forward (eastward) at 5 m/s relative to the jeepney. What is the ball's velocity relative to a stationary observer on the street? (2 PTS)
    1. 25 m/s east
    2. 15 m/s east
    3. 5 m/s east
    4. Cannot be determined without knowing the ball's mass
  4. A particle moves counterclockwise around a circle at constant speed. Which statement correctly describes the relationship between velocity and acceleration? (2 PTS)
    1. Velocity is tangent to the circle; acceleration points toward the center of the circle.
    2. Velocity and acceleration point in the same direction, both tangent to the circle.
    3. Acceleration is tangent to the circle; velocity points toward the center.
    4. Both velocity and acceleration point toward the center of the circle.
  5. A rotating wheel makes 3 complete counterclockwise revolutions in 3 seconds, then reverses direction and makes 1 complete clockwise revolution in 2 seconds. What is the angular velocity during the first 3 seconds? (2 PTS)
    1. 3π rad/s
    2. π rad/s
    3. 2π rad/s
    4. 6π rad/s

True or False

  1. In projectile motion, the horizontal and vertical components of motion are independent of each other. (1 PTS)
  2. The radian is the SI unit of angle and is defined such that an angle of 1 radian corresponds to an arc length equal to the radius of the circle. (1 PTS)
  3. Angular velocity and angular acceleration must have the same sign when an object is rotating faster and faster. (1 PTS)

Problem Solving

  1. ApplyA frog jumps at an angle of 30° above the horizontal with an initial speed of 4.62 m/s. Using the range formula for a projectile that lands at the same elevation from which it was launched, calculate how far the frog jumps. (Use g = 9.80 m/s2.) (5 PTS)
  2. ApplyA projectile is launched with initial velocity components v0x = 9.8 m/s and v0y = 19.6 m/s. Calculate the vertical component of velocity after 1.0 s of flight. (Use g = 9.80 m/s2.) (5 PTS)

Answer key

Multiple Choice

  1. 1.C — The horizontal and vertical components of projectile motion are independent; both balls fall the same vertical distance in the same time regardless of horizontal velocity.
  2. 2.D — The y-component of acceleration is ay = (75 m/s2) sin(25°) = 31.6 m/s2, as shown in the worked example for the spacecraft trajectory.
  3. 3.A — Using the velocity addition formula (vx)CB = (vx)CA + (vx)AB, the ball's velocity relative to the ground is 5 + 20 = 25 m/s east.
  4. 4.A — In uniform circular motion, the velocity is always tangent to the circle, while the centripetal acceleration always points toward the center, making them perpendicular.
  5. 5.C — Three counterclockwise revolutions equal 3 × 2π = 6π rad. The angular velocity is ω = Δθ / Δ t = 6π rad / 3 s = 2π rad/s.

True or False

  1. 1.True — The horizontal velocity remains constant while vertical motion is governed by gravity independently, as stated in the projectile motion principle.
  2. 2.True — By definition, θ(radians) = s/r, where s is arc length and r is radius, so 1 rad occurs when s = r.
  3. 3.True — When rotation is speeding up, ω and α have the same sign; when slowing down, they have opposite signs.

Problem Solving

  1. 1.Use the range formula: range = (v02 sin(2θ))/g. With v0 = 4.62 m/s and θ = 30°: range = ((4.62)2 sin(2 × 30°))/9.80 = (21.34 sin(60°))/9.80 = (21.34 × 0.866)/9.80 = 1.89 m or approximately 1.9 m. — This solution correctly applies the range formula with the given angle and initial speed to find the horizontal distance traveled.
  2. 2.Use the vertical velocity equation: vy = v0y - gΔ t = 19.6 - (9.80)(1.0) = 19.6 - 9.8 = 9.8 m/s. — This solution correctly applies the kinematic equation for vertical velocity, accounting for the constant downward acceleration due to gravity.