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Advanced
Mathematical
GQ

A projectile is launched at an angle of \( 30^{\circ} \) and hits a vertical wall \( 40 \) \( \text{m} \) away. After bouncing back horizontally, it lands \( 15 \) \( \text{m} \) behind the launch point. How high up on the wall did the projectile strike?

Advanced
Mathematical
FRQ

Shown above are three masses of \(6 \, \text{kg}\), \(3 \, \text{kg}\), and \(1 \, \text{kg}\) (in order from left to right). You pull on the 1kg mass with a force \(F\) of \(15 \, \text{N}\) along a frictionless surface.

Intermediate
Conceptual
MCQ

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

Intermediate
Mathematical
GQ

A box is sliding down an incline at a constant speed of \( 2 \, \text{m/s} \). The angle of the incline is \( \theta \). The magnitude of the total of the opposing forces is \( 16 \, \text{N} \). Derive an equation for the force of gravity acting on the box.

Beginner
Proportional Analysis
MCQ

Jill does twice as much work as Jack does and in half the time. Jill’s power output is

Intermediate
Mathematical
GQ

You are piloting a small plane, and you want to reach an airport \(450 \, \text{km}\) due south in \(3.0 \,\text{hours}\). A wind is blowing from the west at \(50.0 \,\text{km/h}\). What heading and airspeed should you choose to reach your destination in time?

Advanced
Mathematical
MCQ

An apple is released from rest \(500 \, \text{m}\) above the ground. Due to the combined forces of air resistance and gravity, it has a speed of \(40 \, \text{m/s}\) when it reaches the ground. What percentage of the initial mechanical energy of the apple–Earth system was dissipated due to air resistance? Take the potential energy of the apple–Earth system to be zero when the apple reaches the ground.

Beginner
Mathematical
GQ

A car accelerates from rest with an acceleration of \( 4.3 \, \text{m/s}^2 \) for a time of \( 6.8 \, \text{s} \). The car then slows to a stop with an acceleration of \( 5.1 \, \text{m/s}^2 \). What is the total distance traveled by the car?

Advanced
Mathematical
GQ

A projectile is launched at \( 20 \) \( \text{m/s} \) and lands \( 35 \) \( \text{m} \) away on level ground. At what two horizontal positions is the projectile exactly \( 5.0 \) \( \text{m} \) above the ground?

Intermediate
Mathematical
GQ

Consider a neutron star with a mass equal to the sun, a radius of 10 km, and a rotation period of 1.0 s. What is the speed of a point on the equator of the star?

Advanced
Conceptual
MCQ

A solid sphere of mass \( M \) and radius \( R \) rolls without slipping down an inclined plane starting from rest. Select all that would affect the angular velocity of the sphere at the bottom of the incline.

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