The correct answer is (E). This is a curvilinear problem. The package already has the x-axis (horizontal) velocity of the plane. Even though the package accelerates toward the ground, its horizontal velocity remains exactly the same as when it left the plane, and that keeps the package moving along under the airplane until it strikes the ground.

The correct answer is (C). An isothermal process is a process in which the temperature of the system remains constant.

The correct answer is (D). Based on Hooke's Law, F = kx where F is mg and x is the elongation. Solving for x = mg/k, so if m is doubled, x is doubled as well.

The correct answer is (C). All forces occur in pairs, are equal in magnitude and oppositely directed. The pairs of forces are the ball on the window, and the window on the ball, which are equal and opposite.

The correct answer is (D). The impulse impressed onto the cart is the same as the momentum the cart achieves. The momentum is given as P = mv, which was given to the cart in a time of .8 sec. The impulse an object receives in a given time is Ft = (delta)P. The solution is found by replacing the P (momentum), yielding the equation Ft = mv, which is rearranged to find the force. F = (m)(v)/t.

The correct answer is (B). One of Kepler's observations in his laws of planetary motion was that the planets orbit the sun in elliptical orbits.

The correct answer is (B). The frequency is the inverse of the period. Lengthening the pendulum increases the length of the period, which means the frequency decreases.

The impulse delivered to the ball, J = ∆t, equals its change in momentum. Thus,

Special relativity says that time dilates for objects moving at relativistic speeds, so the time should be greater (and never change). You could compute the exact value of the time as follows. If v = c, then the relativistic factor is

The equation I = implies that increasing V by a factor of 2 will cause I to increase by a factor of 2.

A nucleus in an excited energy state can relax  to a lower energy state by releasing energy. If the photon(s) emitted in this process are in the gamma-ray portion of the electromagnetic spectrum, we refer to this decay  as gamma decay. The numbers of protons and neutrons remain unchanged.

The correct answer is (D). A net force applied to a body causes the body to be accelerated. This is Sir Isaac Newton's second law of motion, F = ma.

The de Broglie wavelength of a particle whose momentum is p is λ= h/p. For this proton, we find that

The correct answer is (B). This is a problem that requires an Ohm's Law calculation to find resistance. Rearrange the equation to find resistance.

Since the gases are in thermal equilibrium in the same container, they're at the same temperature, and because the average kinetic energy of the molecules is proportional to the temperature, the fact that their temperatures are the same implies that the average kinetic energy of their molecules is the same also. This eliminates A and B. Now, in order for the lighter molecules to have the same average kinetic energy as the heavier ones, the lighter molecules must be moving faster on average, so E is correct.

The correct answer is (B). Since the centripetal force is found with the equation Fc = (m)(v2)/r we can change the r value to .5r and substitute it into the equation and solve to find the relative force. Fc = (m)(v2)/.5r. Clearly the force will be double when the radius is halved and the velocity remains the same.

The correct answer is (B). The heat content of a substance is dependent on three different things, the specific heat of the substance, the mass of the substance, and the temperature of the substance. The specific heat can be disregarded since the substance is the same for both containers. The mass of the water in the cup is less than the mass of the water in the bucket, therefore the cup of water has less heat content than the bucket of water even though they are at the same temperature.

The correct answer is (A). The force down the plane is a component of the weight of the block, which is found by multiplying the weight of the object by the sine θ of the angle to which the plane is raised. This produces a force down the plane, which will accelerate the object when the plane is raised high enough. The frictional force between the block and the plane always acts against the motion of the object-in this case, friction operates up the plane. Since there is no acceleration, the frictional force (Ff) opposing the motion of the block exactly equals the downward force (F11).

When a nucleus undergoes alpha decay, a neutron is converted into a proton and an electron, and the electron is ejected. Because of this, the number of protons in the nucleus ”the atomic number ”is increased by 1.

The magnetic force provides the centripetal force on the charged particle. It follows that

Special relativity dictates that length contracts for objects moving at relativistic speeds, so the length should be smaller. That's C. (Bear in mind that the speed is attainable because the square root of three is less than 2, so the speed is less than the speed of light.) Mathematically, you could calculate the length as follows. If v = ()c, then the relativistic factor is

The correct answer is (B). Once the paperboy releases the paper from his hand, the paper is in free fall. All objects in free fall near the earth experience the same constant acceleration.

The correct answer is (D). The highly polished interior surface of the thermos bottle reflects radiated heat from the substance back into the substance it is keeping hot.

Use the equation that relates wavelength, frequency, and wave speed.

The correct answer is (D). An ideal gas follows Boyle's law. If the pressure increases by a factor of four, the volume decreases by a factor of four. Whatever the change in one, the other is indirectly related by the same factor.

The correct answer is (A). An echo is the repeat sound heard when the original sound waves strike a fixed object and return toward their origin. This is the process of reflection.

The correct answer is (C). The weight of the astronaut is dependent upon the gravitational attraction of the planetary body. Mars has a lower gravitational attraction than the earth, so the astronaut weighs less on Mars. The mass of an object, or a person, is an intrinsic quality of a body that does not change.

The correct answer is (C). Scientists look at the light from a star by passing the light through a spectometer, which separates the starlight into the individual line spectra of the elements that are burning in the star.

The correct answer is (E). Both light and radio waves are electromagnetic radiation. The difference between the two is their frequency.

Kepler's Third Law says that T2 ∝ R3 for a planet with a circular orbit of radius R. Since T ∝ , if R increases by a factor of 9, then T increases by a factor of

The correct answer is (A). The number of protons and the atomic number are the same quantity. The Z number represents the atomic number.

First draw a free-body diagram.

Perhaps the easiest way answer this question is to choose a numerical value for the distance between X and Y. Let's choose 180 m. Then the time it takes the athlete to run from X to Y is 60 seconds, and the time it takes to run from Y back to X is 30 seconds. Her average speed for the entire run is the total distance traveled, 180 m + 180 m = 360 m, divided by the total time, 60 s + 30 s = 90 s. This gives an average speed for the entire trip of (360 m)/(90 s) = 4 m/s. (Note: You would get the same answer, 4 m/s, no matter what positive value you chose for the distance between X and Y.)

The correct answer is (C). The black disk absorbs heat better than the white disk, and it radiates heat away faster.

The correct answer is (B). The binding energy is the result of the conversion of the mass defect into the energy that holds the protons in the nucleus in spite of their repulsion for each other.

The correct answer is (C). To solve the problem you must first find the equivalent resistance of the two parallel resistors. The resistors are the same value; so divide 30 ohms by 2, which gives a value of 15 ohms. Add 15 ohms to the 9 ohms in series with the parallel resistors for a total resistance of 24 ohms. The voltage is equal to the current multiplied by the resistance, Ohm's Law. (24ohm)(.25) = 6 V.

The correct answer is (E). Without more information about the applied force, all of the choices could be correct.

The correct answer is (C). When the voltage is disconnected there is a small lag time between the disconnection of the current and the ceasing of the flow because the magnetic field, which is induced into the wires, collapses. This produces a current flow that causes the spark.

Since the acceleration of the projectile is always downward (because it's gravitational acceleration), the vertical speed decreases as the projectile rises and increases as the projectile falls. A is false because the acceleration vector is straight down, but the velocity is never straight up or straight down. It would be true of the vertical component of the velocity, but not of the total velocity. B is false because the projectile still has its horizontal velocity at the top of the trajectory. C is false because the vertical component of the velocity changes, even if the horizontal component does not, so the total speed changes. D is false because the horizontal component is constant throughout the motion.

A bi-concave lens is a diverging lens. Diverging lenses (like convex mirrors) have negative focal lengths and therefore cannot form real images. (Notice that D is false; diverging lenses and convex mirrors always form diminished, virtual images, as you can verify using the mirror and magnification equations.)