Q4. The figure shows three vectors, \( \vec{A} \), \( \vec{B} \), and \( \vec{C} \), along with their magnitudes. Determine the magnitude and direction of the vector given by \( \vec{A} - \vec{B} - \vec{C} \).

Background

Topic: Vector Addition and Subtraction

This question tests your ability to use vector components to add and subtract vectors, and then find the magnitude and direction of the resulting vector.

Key Terms and Formulas

• Vector components: Each vector can be broken into x and y components.

• Resultant vector: The sum or difference of vectors, calculated component-wise.

• Magnitude:

• Direction:

Step-by-Step Guidance

1. Break each vector into its x and y components. Use trigonometry for \( \vec{C} \): , , , (since \( \vec{C} \) points down and left)

2. Calculate the numerical values for \( C_x \) and \( C_y \):

3. Set up the subtraction: \( \vec{A} - \vec{B} - \vec{C} \) means subtracting each component:

4. Plug in the values for each component and simplify to get \( R_x \) and \( R_y \).

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Q14. A projectile is fired from the edge of a cliff as shown in the figure. The initial velocity components are 940 m/s (horizontal) and 96 m/s (vertical). The projectile reaches maximum height at point P and then falls and strikes the ground at point Q. How high is point P above point Q, assuming no air resistance?

Background

Topic: Projectile Motion (Vertical Displacement)

This question tests your understanding of how to calculate the maximum height reached by a projectile, given its initial vertical velocity.

Key Terms and Formulas

• Maximum height:

• : Initial vertical velocity

• : Acceleration due to gravity (9.8 m/s2)

Step-by-Step Guidance

1. Identify the initial vertical velocity: m/s.

2. Recall the formula for maximum height above the starting point: .

3. Plug in the values for and into the formula.

4. Calculate to find the height difference between P and Q.

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Q35. The motions of a car and a truck along a straight road are represented by the velocity-time graphs in the figure. The two vehicles are initially alongside each other at time t = 0. At time T, what is true about these two vehicles since time t = 0?

Background

Topic: Graphical Analysis of Motion

This question tests your ability to interpret velocity-time graphs and compare the distances traveled by two objects.

Key Terms and Formulas

• Velocity-time graph: The area under the curve represents displacement.

• Constant velocity: Horizontal line on the graph.

• Increasing velocity: Sloped line on the graph.

Step-by-Step Guidance

1. Observe the graph: The truck has constant velocity, while the car's velocity increases linearly.

2. Recall that the area under each curve (from t = 0 to t = T) represents the distance traveled by each vehicle.

3. Compare the areas: For the truck, it's a rectangle; for the car, it's a triangle.

4. Think about which area is larger at time T, and what that means for the distance traveled.

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Q38. The figure shows the position of an object as a function of time. During the time interval from t = 0.0 s to t = 9.0 s: (a) What is the length of the path the object followed? (b) What is the displacement of the object?

Background

Topic: Kinematics – Distance vs. Displacement

This question tests your ability to distinguish between the total path length (distance) and displacement (straight-line change in position).

Key Terms and Formulas

• Distance: Total length of the path traveled.

• Displacement: Straight-line distance from initial to final position.

Step-by-Step Guidance

1. Read the graph to determine the object's position at each time interval.

2. Calculate the total path length by summing the segments where the object moves.

3. Find the displacement by subtracting the initial position from the final position.

4. Compare the two values to understand the difference between distance and displacement.

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Q55. The motion of a particle is described in the velocity vs. time graph shown in the figure. Over the nine-second interval shown, we can say that the speed of the particle:

Background

Topic: Velocity-Time Graphs and Speed Analysis

This question tests your ability to interpret a velocity-time graph and describe how the speed of a particle changes over time.

Key Terms and Formulas

• Speed: The magnitude of velocity (always positive).

• Velocity-time graph: Shows how velocity changes with time.

Step-by-Step Guidance

1. Observe the graph: The velocity starts negative and increases to positive values.

2. Recall that speed is the absolute value of velocity.

3. Describe how the speed changes: As velocity moves from negative to positive, the speed decreases (approaching zero), then increases again.

4. Think about the physical meaning: The particle slows down, stops, then speeds up in the opposite direction.

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Q69. Two boxes, A and B, are connected by a horizontal string S on a horizontal floor. A very light wire pulls horizontally on box B, as shown in the figure, with a force of 100 N. The reaction force to this pull is:

Background

Topic: Newton's Third Law (Action-Reaction Pairs)

This question tests your understanding of action-reaction pairs in Newton's laws.

Key Terms and Formulas

• Newton's Third Law: For every action, there is an equal and opposite reaction.

• Action-reaction pair: Forces that are equal in magnitude and opposite in direction, acting on different objects.

Step-by-Step Guidance

1. Identify the force: The wire pulls on box B with 100 N.

2. Recall Newton's Third Law: The reaction force is exerted by box B on the wire.

3. Think about the direction and magnitude of the reaction force.

4. Make sure you understand which objects are involved in the action-reaction pair.

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Q71. In the figure, block A has a mass of 3.00 kg. It rests on a smooth horizontal table and is connected by a very light horizontal string over an ideal pulley to block B, which has a mass of 2.00 kg. When block B is gently released from rest, how long does it take block B to travel 80.0 cm?

Background

Topic: Multiple-Object Accelerating Systems (Atwood Machine)

This question tests your ability to analyze a system of connected masses and calculate the time for a given displacement.

Key Terms and Formulas

• Acceleration: (for frictionless Atwood machine)

• Displacement: (starting from rest)

• Masses: (on table), (hanging)

Step-by-Step Guidance

1. Calculate the acceleration of the system using the formula for an Atwood machine.

2. Set up the kinematic equation for displacement: .

3. Plug in the values for (0.80 m) and (from step 1).

4. Rearrange the equation to solve for .

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