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Intermediate
Mathematical
GQ

On a strange, airless planet, a ball is thrown downward from a height of \( 17 \, \text{m} \). The ball initially travels at \( 15 \, \text{m/s} \). If the ball hits the ground in \( 1 \, \text{s} \), what is this planet’s gravitational acceleration?

Intermediate
Mathematical
FRQ
A right-triangle ramp is drawn on the left side of a horizontal baseline. The ramp’s hypotenuse slopes downward from left to right at an angle labeled “θ0” between the hypotenuse and the rightward horizontal baseline. The horizontal run of the ramp (its base) is marked as length D, starting at x = –D on the leftmost top point of the ramp and ending at x = 0 at the foot of the ramp. From x = 0 to x = 4D, the baseline is a straight horizontal line representing the rough surface. Tick marks on the baseline indicate positions x = 0, D, 2D, 3D, and 4D. The inclined segment is frictionless; the horizontal segment is shaded or marked as rough. No block is explicitly drawn on the diagram.

A block is initially at rest on top of an inclined ramp that makes an angle \( \theta_0 \) with the horizontal. The distance measured along the base of the ramp is \( D \). After the block is released from rest, it slides down the frictionless ramp and then continues onto a rough horizontal surface until it finally comes to rest at the position \( x = 4D \) measured from the base of the ramp. The coefficient of kinetic friction between the block and the rough horizontal surface is \( \mu_k \).

Advanced
Mathematical
GQ

A baseball rolls off a 0.70 m high desk and strikes the floor 0.25 m away from the base of the desk. How fast was the ball rolling?

Intermediate
Conceptual
MCQ

You are lying in bed and want to shut your bedroom door. You have a bouncy “superball” and a blob of clay, both with the same mass \( m \). Which one would be more effective to throw at your door to close it?

Intermediate
Mathematical
GQ

A 150-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope.

What constant force must be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.500 rev/s in 2.00 s?

Note: \( I_\text{disk} = \frac{1}{2}mr^2 \)

Intermediate
Mathematical
MCQ

A 1.0-kg object is moving with a velocity of 6.0 m/s to the right. It collides and sticks to a 2.0-kg object moving with a velocity of 3.0 m/s in the same direction. How much kinetic energy was lost in the collision?

Beginner
Mathematical
GQ

A person stands on a scale in an elevator. If the scale reads \( 600 \, \text{N} \) when that person is riding upward at a constant velocity of \( 4 \, \text{m/s} \), what is the scale reading when the elevator is at rest? Hint: The reading on the scale is simply the normal force.

Intermediate
Mathematical
MCQ

An object is moving at constant velocity. Which of the following could be the free-body diagram representing the forces acting on the object?

Advanced
Mathematical
FRQ

A javelin thrower standing at rest holds the center of the javelin behind her head, then accelerates it through a distance of \( 70 \, \text{cm} \) as she throws. She releases the \( 600 \, \text{g} \) javelin \( 2.0 \, \text{m} \) above the ground traveling at an angle of \( 30^\circ \) above the horizontal. In this throw, the javelin hits the ground \( 54 \, \text{m} \) away. Find the following:

Intermediate
Mathematical
MCQ

A 0.5 kg pendulum bob is raised to 1.0 m above the floor, as shown in the figure. The bob is then released from rest. When the bob is 0.8 m above the floor, its speed is most nearly

Intermediate
Proportional Analysis
GQ

A car is safely negotiating an unbanked circular turn at a speed of 21 m/s. The road is dry, and the maximum static frictional force acts on the tires. Suddenly a wet patch in the road decreases the maximum static frictional force to one-third its dry road value. If the car is to continue safely around the curve, to what speed must the driver slow the car?

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