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Beginner
Mathematical
MCQ

A student walks \( 3 \) \( \text{m} \) east, then \( 4 \) \( \text{m} \) west in \( 7 \) \( \text{s} \). What is their displacement and average velocity?

Intermediate
Mathematical
FRQ

A train is moving to the right at \( 20 \) \( \text{m/s} \). A passenger on the train throws a ball horizontally to the left at \( 5 \) \( \text{m/s} \) (relative to the train).

Intermediate
Mathematical
MCQ

Four identical lead balls with large mass are connected by rigid but very light rods in the square configuration shown in the preceding figure. The balls are rotated about the three labeled axes. Which of the following correctly ranks the rotational inertia \(I\) of the balls about each axis?

Advanced
Proportional Analysis
MCQ

A rocket of mass \( m \) is launched with kinetic energy \( K_0 \), from the surface of the Earth. How much less kinetic energy does the rocket have at an altitude of two Earth radii? Give your answer in terms of the gravitational constant \( G \), the mass of the Earth \( m_E \), the radius of the Earth \( R_E \), and the mass of the rocket?

Intermediate
Conceptual
MCQ

If a constant net torque is applied to an object it will (select all that applies):

Advanced
Mathematical
MCQ

A ring is pulled on by three forces. If the ring is not moving, how big is the force [katex]F[/katex]?

Intermediate
Conceptual
GQ

Water balloons are tossed from the roof of a building, all with the same speed but with different launch angles. Which one has the highest speed when it hits the ground? Ignore air resistance. Without using equations, explain your answer.

Intermediate
Mathematical
GQ

A solid titanium sphere of radius \( 0.35 \) \( \text{m} \) has a density \( 4500 \) \( \text{kg/m}^3 \). It is held suspended completely underwater by a cable. What is the tension in the cable?

Beginner
Conceptual
MCQ

A moderate force will break an egg. However, an egg dropped on the road usually breaks, while one dropped on the grass usually does not break because for the egg dropped on the grass:

Beginner
Conceptual
GQ

What would your bathroom scale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at an angle.

Intermediate
Conceptual
MCQ

Projectiles 1 and 2 are launched from level ground at the same time and follow the trajectories shown in the figure. Which one of the projectiles, if either, returns to the ground first, and why?

Intermediate
Mathematical
MCQ

Alcohol has a specific gravity of \( 0.79 \). If a barometer consisting of an open-ended tube placed in a dish of alcohol is used at sea level, to what height in the tube will the alcohol rise?

Intermediate
Mathematical
GQ

A bald eagle in level flight at a height of \(135 \, \text{m}\) drops the fish it caught. If the eagle’s speed is \(25.0 \, \text{m/s}\) how far from the drop point will the fish land?

Intermediate
Mathematical
FRQ

Ball A is dropped from the top of a cliff. At the same time, Ball B is thrown straight upward from the ground at \( 30 \) \( \text{m/s} \). The two balls pass each other after \( 2.0 \) \( \text{s} \).

Beginner
Mathematical
MCQ

An object weighing 120 N is set on a rigid beam of negligible mass at a distance of 3 m from a pivot, as shown above. A vertical force is to be applied to the other end of the beam a distance of 4 m from the pivot to keep the beam at rest and horizontal. What is the magnitude F of the force required?

Beginner
Mathematical
GQ

Two students start \( 100 \) \( \text{m} \) apart.

• Student A walks to the right at \( 2 \) \( \text{m/s} \).

• Student B walks to the left at \( 3 \) \( \text{m/s} \).

At what time do the students meet, and how far has each student walked when they collide?

Intermediate
Mathematical
GQ

An \(80 \, \text{kg}\) person sits on a swing ride that moves in a horizontal circle. The swing is suspended by a chain of length \(8 \, \text{m}\). While in motion, the chain makes a \(40^\circ\) angle with the horizontal. What is the speed of the person?

Advanced
Mathematical
GQ

A diver springs upward from a diving board. At the instant she contacts the water, her speed is \( 8.90 \, \text{m/s} \), and her body is extended at an angle of \( 75.0^\circ \) with respect to the horizontal surface of the water. At this instant, her vertical displacement is \( -3.00 \, \text{m} \), where downward is the negative direction. Determine her initial velocity, both magnitude and direction.

Intermediate
Mathematical
MCQ

A mass is attached to a spring of spring constant 60 N/m along a horizontal, frictionless surface. The spring is initially stretched by a force of 5.0 N and let go. It takes the mass 0.50 s to go back to its equilibrium position when it is oscillating. What is the amplitude?

Intermediate
Proportional Analysis
MCQ

Two balls are dropped from the roof of a building. One ball has twice as massive as the other and air resistance is negligible. Just before hitting the ground, the more massive ball has ball  ____ the kinetic energy of the less massive ball.

Intermediate
Mathematical
MCQ

In the lab, a student is given a glass beaker filled with water with an ice cube of mass \( m \) and volume \( V_c \) floating in it.

The downward force of gravity on the ice cube has magnitude \( F_g \). The student pushes down on the ice cube with a force of magnitude \( F_P \) so that the cube is totally submerged. The water then exerts an upward buoyant force on the ice cube of magnitude \( F_B \). Which of the following is an expression for the magnitude of the acceleration of the ice cube when it is released?

Beginner
Mathematical
FRQ

An airliner arrives at the terminal, and the engines are shut off. The rotor of one of the engines has an initial clockwise angular velocity of \( 2000 \) \( \text{rad/s} \). The engine’s rotation slows with an angular acceleration of magnitude \( 80.0 \) \( \text{rad/s}^2 \).

Beginner
Conceptual
MCQ

In which of the following cases does a car have a negative velocity and a positive acceleration? A car that is traveling in the:

Intermediate
Mathematical
FRQ

An airplane is traveling \( 900. \) \( \text{km/h} \) in a direction \( 38.5^\circ \) west of north.

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