Two clouds collide and form another, more massive cloud. One cloud is stationary, while the other is traveling at $1 \mathrm{~m} / \mathrm{s}$. After the collision, the new, combined cloud travels with a velocity of $0.25 \mathrm{~m} / \mathrm{s}$. What is the ratio of the masses of the two original clouds?

A $15,000 \mathrm{~kg}$ rocket traveling at $+230 \mathrm{~m} / \mathrm{s}$ turns on its engines. Over a $6.0 \mathrm{~s}$ period it burns $1,000 \mathrm{~kg}$ of fuel. An observer on the ground measures the velocity of the expelled gases to be $-1,200 \mathrm{~m} / \mathrm{s}$.
a What is the resulting speed of the rocket after the burn?
b. What is the acceleration of the rocket during the burn? Express your answer in meters per second squared and in " $g$s.
c. What impulse is applied to the rocket?

Nina, whose mass is $60 \mathrm{~kg}$, is traveling on a bike at $15 \mathrm{~m} / \mathrm{s}$ at the top of a $3.0 \mathrm{~m}$ hill. Nina continues down this hill without pedaling. Assume friction is negligible.
a. What energy transformation is occurring as she travels down the hill?
b. How fast is she traveling when she reaches the bottom of the hill?

If In an elastic collision, a $1.0 \mathrm{~kg}$ ball moving at $1.0 \mathrm{~m} / \mathrm{s}$ collides with a $2.0 \mathrm{~kg}$ ball moving at $-2.0 \mathrm{~m} / \mathrm{s}$. The $2.0 \mathrm{~kg}$ ball transfers all of its momenta to the $1.0 \mathrm{~kg}$ ball.
a. What velocity does the $1.0 \mathrm{~kg}$ ball have after the collision?
b. What is the initial kinetic energy of the system?
c. What is the final kinetic energy of the system?

A stationary $165 \mathrm{~kg}$ football player is tackled by a $178 \mathrm{~kg}$ player running at $8 \mathrm{~m} / \mathrm{s}$
a. How fast are they moving after the collision?
b. What is the impulse imparted on the stationary player?
c. What is the impulse imparted on the moving player?

A 0.21-kg apple falls from a tree to the ground, 4.0 m below. Ignoring air resistance, determine the apple's kinetic energy, KE, the gravitational potential energy of the system, PE$_{\mathrm{gravity}}$, and the total mechanical energy of the system, E, when the apple's height above the ground is 3.0 m.

In a tennis match a player wins a point by hitting the 0.059-kg ball sharply to the ground on the opponent's side of the net. If the ball bounces upward from the ground with a speed of 16 m/s and is caught by a fan in the stands when it has a speed of 12 m/s, how high above the court is the fan? Ignore air resistance.

If the mass of the ball were increased, would its speed just before it is caught be greater than, less than, or the same as the value we just found? Assume that everything else remains the same.

A $2,000 \mathrm{~kg}$ car moving at $10 \mathrm{~m} / \mathrm{s}$ collides head-on with a $2,500 \mathrm{~kg}$ car moving in the opposite direction at $15 \mathrm{~m} / \mathrm{s}$. The two cars are locked together after impact.
a. Is this an elastic or an inelastic collision? Why?
b. What is the speed of the cars after impact?
c. Calculate the kinetic energies of the cars, both before and after impact.
d. What fraction of the kinetic energy was lost during the impact? Where did the energy go?

If A $2.0 \mathrm{~kg}$ puck is moving east at $5.5 \mathrm{~m} / \mathrm{s}$. It catches up to and collides with a second identical puck moving due east at $3.0 \mathrm{~m} / \mathrm{s}$. The collision is perfectly inelastic.

a. What is the resulting velocity of the pucks?
b. What is the initial kinetic energy $E_{k i}$ of the system?
c. What is the change in kinetic energy, $\Delta E_k$, of the system as a result of the collision?
d. If the mass $m$ is doubled, but the initial velocities are unchanged, does the resulting velocity increase, decrease, or remain unchanged?

A $10,000 \mathrm{~kg}$ railroad car traveling north at $10 \mathrm{~m} / \mathrm{s}$ collides with a $5,000 \mathrm{~kg}$ rail car also moving north but at an unknown speed. After the collision, the two cars lock together and move north at $8 \mathrm{~m} / \mathrm{s}$. How fast was the second car moving before the impact?

A $1,200 \mathrm{~kg}$ car is heading due north at $14.0 \mathrm{~m} / \mathrm{s}$. It collides with an identical car heading due south at $14.0 \mathrm{~m} / \mathrm{s}$. What is the combined momentum of the cars before the collision?

A collision where the objects stick together after impact is called a/an

Comets move in highly elliptical orbits. For example, the aphelion, or farthest point of Comet Hale-Bopp's orbit is 371 AU from the Sun. The perihelion, or closest approach, is $0.91 \mathrm{AU}$, within the Earth's orbital radius!
a. Use the orbit equation to calculate the velocity of Comet Hale-Bopp at aphelion.
b. Use the orbit equation to calculate the velocity of Comet Hale-Bopp at perihelion.