Q: A projectile is launched at an angle $$\theta$$ above the horizontal with an initial speed $$v_0. $$Which of the following equations gives the maximum height $$H$$ reached by the projectile?

$$H = \frac{v_0$^2 \sin^2$ \theta}{2g}$$

Question 1

A projectile is launched at an angle $$	heta$$ above the horizontal with an initial speed $$v_0. $$Which of the following equations gives the maximum height $$H$$ reached by the projectile?

Accepted Answer

$$H = \frac{v_0$^2 \sin^2$ 	heta}{2g}$$

Question 2

Which of the following best describes the difference between a vector and a scalar?

Accepted Answer

A vector has both magnitude and direction, while a scalar has only magnitude.

Question 3

A car moves with a constant velocity of $$20\ \mathrm{m/s}$$ east for $$10\ \mathrm{s}$$, then turns and moves $$20\ \mathrm{m/s}$$ north for $$10\ \mathrm{s}. $$What is the magnitude of the car's displacement from its starting point?

Accepted Answer

$$282.8\ \mathrm{m}$$

Question 4

Which equation correctly expresses the work done $$W by a $$constant force $$F$$ acting over a displacement $$d at an $$angle $$	heta to $$the direction of the force?

Accepted Answer

$$W = Fd \cos 	heta$$

Question 5

A $$2\ \mathrm{kg}$$ block slides down a frictionless incline of height $$5\ \mathrm{m}. $$What is its speed at the bottom? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$9.9\ \mathrm{m/s}$$

Question 6

Which of the following is a correct statement of the law of conservation of energy?

Accepted Answer

Energy cannot be created or destroyed, only transformed from one form to another.

Question 7

A $$0.5\ \mathrm{kg}$$ ball moving at $$4\ \mathrm{m/s}$$ collides elastically with a stationary $$0.5\ \mathrm{kg}$$ ball. What is the velocity of the first ball after the collision?

Accepted Answer

$$0\ \mathrm{m/s} (it $$stops and the second ball moves at $$4\ \mathrm{m/s})$$

Question 8

Which equation gives the period $$T of a $$simple pendulum of length $$L$$?

Accepted Answer

$$T = 2\pi \sqrt{\frac{L}{g}}$$

Question 9

A $$3\ \mathrm{kg}$$ object moving at $$2\ \mathrm{m/s}$$ collides inelastically with a $$2\ \mathrm{kg}$$ object at rest. What is the final velocity of the combined mass?

Accepted Answer

$$1.2\ \mathrm{m/s}$$

Question 10

Which of the following best describes the torque $$	au$$ produced by a force $$F$$ applied at a distance $$r$$ from the axis of rotation at an angle $$	heta$$?

Accepted Answer

$$	au = rF \sin 	heta$$

Question 11

A $$0.2\ \mathrm{kg}$$ mass attached to a spring oscillates with a period of $$0.5\ \mathrm{s}. $$What is the spring constant $$k$$?

Accepted Answer

$$63.2\ \mathrm{N/m}$$

Question 12

Which of the following describes the energy transported by a wave?

Accepted Answer

It is proportional to the square of the amplitude.

Question 13

A $$5\ \mathrm{kg}$$ disk rotates with a constant angular acceleration $$\alpha = 2\ \mathrm{$$rad/s^2$$}. $$What is the angular velocity after $$3\ \mathrm{s} if it $$starts from rest?

Accepted Answer

$$6\ \mathrm{rad/s}$$

Question 14

Which of the following is true for the center of mass of a system of particles?

Accepted Answer

It moves as if all the mass and external forces are concentrated at that point.

Question 15

A $$0.1\ \mathrm{kg}$$ ball moving at $$10\ \mathrm{m/s}$$ collides elastically with a $$0.2\ \mathrm{kg}$$ ball at rest. What is the velocity of the $$0.1\ \mathrm{kg}$$ ball after the collision?

Accepted Answer

$$-3.3\ \mathrm{m/s}$$

Question 16

Which equation gives the kinetic energy $$K of an $$object of mass $$m$$ moving at speed $$v$$?

Accepted Answer

$$K = \frac{1}{2}mv^2$

Question 17

A wave on a string has a frequency of $$50\ \mathrm{Hz}$$ and a wavelength of $$2\ \mathrm{m}. $$What is its speed?

Accepted Answer

$$100\ \mathrm{m/s}$$

Question 18

Which of the following best describes resonance in a standing wave?

Accepted Answer

It occurs when the frequency of a driving force matches a natural frequency of the system.

Question 19

A $$0.5\ \mathrm{kg}$$ mass attached to a spring oscillates with an amplitude of $$0.1\ \mathrm{m}$$ and a period of $$1\ \mathrm{s}. $$What is its maximum speed?

Accepted Answer

$$0.628\ \mathrm{m/s}$$

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