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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?
An object has a mass of \(10 \, \text{kg}\). For each case below answer the questions and provide an example.
A drinking fountain projects water at an initial angle of \( 50^ \circ \) above the horizontal, and the water reaches a maximum height of \( 0.150 \) \( \text{m} \) above the point of exit. Assume air resistance is negligible.
A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round. As he does this, it is true to say that
A \(15 \, \text{g}\) marble moves to the right at \(3.5 \, \text{m/s}\) and makes an elastic head-on collision with a \(22 \, \text{g}\) marble. The final velocity of the \(22 \, \text{g}\) marble is \(2.0 \, \text{m/s}\) to the right, and the final velocity of the \(15 \, \text{g}\) marble is \(5.4 \, \text{m/s}\) to the left. What was the initial velocity of the \(22 \, \text{g}\) marble?
A plane, 220 meters high, is dropping a supply crate to an island below. It is traveling with a horizontal velocity of 150 m/s. At what horizontal distance must the plane drop the supply crate for it to land on the island? Use \( g = 9.81 \, m/s^2\).
If an object is moving, is it possible for the net force acting on it to be zero? Explain.
A \(0.10 \, \text{kg}\) ball, traveling horizontally at \(25 \, \text{m/s}\), strikes a wall and rebounds at \(19 \, \text{m/s}\). What is the magnitude of the change in the momentum of the ball during the rebound?
The gravitational force that the Moon exerts on Earth is often cited as the source of the tides we witness. However, the gravitational force the Sun exerts on Earth is over \(100\) times greater than the force the Moon exerts on Earth.
Why is the force from the Moon credited for the tides, and not the force from the Sun?
Water of density \( \rho \) flows through the section of circular pipe shown in the figure. At Point A, where the diameter of the pipe is \( D \), the water has a pressure \( P_0 \) and velocity \( v_0 \). Point B is located a vertical distance \( H \) above Point A in a section of the pipe that has diameter \( 2D \).
Which of the following expressions is equal to the pressure of the water at Point B?
Imagine a hypothetical planet that has two moons. Moon \(\#1\) is in a circular orbit of radius \(R\) and has a mass \(M\).
An ice skater that is spinning in circles has an initial rotational inertia \(I_i\). You can approximate her shape to be a cylinder. She is spinning with velocity \(\omega_i\). As she extends her arms, her rotational inertia changes by a factor of \(x\) and her angular velocity changes by a factor of \(y\). Which one of the following options best describe \(x\) and \(y\)?
Two balls are thrown off a building with the same speed, one straight up and one at a 45° angle. Which statement is true if air resistance can be ignored?
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?
A \( 15 \) \( \text{N} \) force is pushing a \( 40 \) \( \text{N} \) block down a incline. The angle of the inline is \( \alpha = 40^{\circ} \). The coefficient of static friction between the block and the incline is \( \mu_s = 0.75 \) and the coefficient of kinetic friction is \( \mu_k = 0.65 \).
A Venturi tube has a pressure difference of \( 15\,000 \) \( \text{Pa} \). The entrance radius is \( 3 \) \( \text{cm} \), while the exit radius is \( 1 \) \( \text{cm} \). What are the entrance velocity, exit velocity, and flow rate if the fluid is gasoline \( (\rho = 700 \) \( \text{kg/m}^3 ) \)?
An object undergoing simple harmonic motion has a maximum displacement of \(6.2\) \(\text{m}\) at \(t = 0.0\) \(\text{s}\). If the angular frequency of oscillation is \(1.6\) \(\text{rad/s}\), what is the object’s displacement when \(t = 3.5\) \(\text{s}\)?
A block of mass \(M_1\) travels horizontally with a constant speed \(v_0\) on a plateau of height \(H\) until it comes to a cliff. A toboggan of mass \(M_2\) is positioned on level ground below the cliff. The center of the toboggan is a distance \(D\) from the base of the cliff.
A theme park ride consists of a large vertical wheel of radius \( R \) that rotates counterclockwise on a horizontal axle through its center. The cars on the wheel move at a constant speed \( v \). Points \( A \) and \( D \) represent the position of a car at the highest and lowest point of the ride, respectively. While passing point \( A \), a student releases a small rock of mass \( m \), which falls to the ground without hitting anything. Which of the following best represents the kinetic energy of the rock when it is at the same height as point \( D \)?
A golfer hits her ball in a high arcing shot. Air resistance is negligible. When the ball is at its highest point, which of the following is true?
A pool cue ball, mass \(0.7 \, \text{kg}\), is traveling at \(2 \, \text{m/s}\) when it collides head-on with another ball, mass \(0.5 \, \text{kg}\), traveling in the opposite direction with a speed of \(1.2 \, \text{m/s}\). After the collision, the cue ball travels in the opposite direction at \(0.3 \, \text{m/s}\). What is the velocity of the other ball?
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?
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:
A car traveling to the right with a speed \( v \) brakes to a stop in a distance \( d \). What is the work done on the car by the frictional force \( F \)? (Assume that the frictional force is constant)
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