Three people are observing the same car. One person claims that the car’s momentum is positive, another person claims that it is negative, and the third person says that it is zero. Can they all be right at the same time? Explain.

Describe two experiments that you can perform to determine the focal length of a glass convex lens. Is it a converging or a diverging lens? How do you know?

When would a ball hitting a wall have a greater change in momentum: when it hits the wall and bounces back at the same speed or when it hits and sticks to the wall? Explain your answer.

In this exercise, we define the first difference

$$\delta f$$

of a function f by

$$\delta f ( x ) = f ( x + 1 ) - f ( x ).$$

Show that for any two functions f and g,

$$\delta ( f + g ) = \delta f + \delta g$$

and

$$\delta ( c f ) = c \delta ( f ),$$

where c is any constant.

Construct impulse-momentum bar charts to represent a falling ball in (a) a system whose momentum is not constant and (b) a system whose momentum is constant. In the initial state, the ball is at rest; in the final state, the ball is moving.

Choose an example in which the momentum of a system is not constant.(a) A bullet shot from a rifle, with the rifle and the bullet as the system (b) A freely falling metal ball, with the ball as the system (c) A freely falling metal ball, with the ball and Earth as the system (d) It is not possible to give an example since the momentum of a system is always constant.

Why does an inflated balloon shoot across a room when air is released from it?(a) Because the outside air pushes on the balloon (b) Because the momentum of the balloon-air system is constant (c) Because the air inside the balloon pushes on the balloon, exerting the same force that the balloon exerts on the air (d) Both b and c are correct.

Let $S$ be a spanning set for $V$. Show that the vector $\mathbf{u}$ is in $V^{\perp}$ if and only if $\mathbf{u}$ is orthogonal to every vector in $S$.

John drew a right triangle with sides 6 inches, 8 inches, and 10 inches long. What was the area of the triangle?

Impulse (a) is the time rate of change of momentum, (b) is the force per unit time, (c) has the same units as momentum, (d) none of these.

What economic and political developments weakened the Republican Party during Grant's second term?

Describe the function of the gallbladder.

In 2009, there were 14,100 students at college A, with a projected enrollment increase of 1500 students per year. In the same year, there were 41,700 students at college B, with a projected enrollment decline of 800 students per year. In which year will the colleges have the same enrollment? What will be the enrollment in each college at that time?

Use a graphic organizer to note the political measures that Lincoln took to solve problems he faced during the war.