Q: A projectile is launched from level ground with initial speed $ v_0 $ at an angle $ \theta_0 $. What is the formula for its range (horizontal displacement) ignoring air resistance?

$R = \frac{v_0^2 \sin 2\theta_0}{g}$

Q: If a vector $ \vec{A} $ is multiplied by a scalar $ c = -1 $, what happens to the resulting vector $ \vec{B} $?

It points in the opposite direction to $ \vec{A} $ but has the same magnitude.

Question 1

A vector $ \vec{A} $ has components $ (3, 4, 0) $. If it is multiplied by a scalar $ c = -2 $, what are the components of the resulting vector $ \vec{B} $?

Accepted Answer

$(-6, -8, 0)$

Question 2

Which of the following statements about vector addition is correct?

Accepted Answer

The sum of vectors is the same regardless of the order of addition.

Question 3

A projectile is launched from level ground with initial speed $ v_0 $ at an angle $ \theta_0 $. What is the formula for its range (horizontal displacement) ignoring air resistance?

Accepted Answer

$R = \frac{v_0^2 \sin 2	heta_0}{g}$

Question 4

If a vector $ \vec{A} $ is multiplied by a scalar $ c = -1 $, what happens to the resulting vector $ \vec{B} $?

Accepted Answer

It points in the opposite direction to $ \vec{A} $ but has the same magnitude.

Question 5

A train moves east at $ 20 \ \mathrm{m/s} $ relative to the ground. A passenger walks west inside the train at $ 2 \ \mathrm{m/s} $ relative to the train. What is the passenger's velocity relative to the ground?

Accepted Answer

$v_{passenger/ground} = 18 \ \mathrm{m/s}$ \ east

Question 6

Which of the following is true about the effect of air resistance on projectile motion?

Accepted Answer

Air resistance reduces the maximum height and range, and makes the path asymmetrical.

Question 7

Given the initial velocity components $ v_{0x} = 5 \ \mathrm{m/s} $ and $ v_{0y} = 8 \ \mathrm{m/s} $, what is the magnitude of the initial velocity $ v_0 $?

Accepted Answer

$v_0 = \sqrt{5^2 + 8^2} = 9.43 \ \mathrm{m/s}$

Question 8

Which of the following best describes the difference between mass and weight?

Accepted Answer

Mass is a measure of the amount of matter, while weight is the gravitational force acting on that mass.

Question 9

A block slides on a horizontal surface. Which statement about the friction force acting on the block is correct?

Accepted Answer

Friction acts opposite to the direction of relative motion between surfaces.

Question 10

A ball is thrown upward with initial velocity $ v_0 $. What is its velocity at the highest point of its trajectory?

Accepted Answer

$v = 0$

Question 11

Which equation correctly gives the vertical component of velocity for a projectile at time $ t $?

Accepted Answer

$v_y = v_{0y} - g t$

Question 12

If a vector $ \vec{A} $ is multiplied by a scalar $ c = 0 $, what is the result?

Accepted Answer

A zero-length vector with no direction.

Question 13

A car moves north at $ 15 \ \mathrm{m/s} $ relative to the ground. A person walks south inside the car at $ 3 \ \mathrm{m/s} $ relative to the car. What is the person's velocity relative to the ground?

Accepted Answer

$v_{person/ground} = 12 \ \mathrm{m/s}$ \ north

Question 14

Which of the following is a correct statement about the graphical method for adding vectors?

Accepted Answer

Draw each subsequent vector starting from the tip of the previous vector.

Question 15

A spring is stretched by a force $ F $ and obeys Hooke's Law. What is the relationship between the force and the displacement $ x $?

Accepted Answer

$F = kx$

Question 16

Which of the following is NOT a vector quantity?

Accepted Answer

Mass

Question 17

If a projectile is launched at $ \theta_0 = 45^\circ $ with initial speed $ v_0 $, what happens to its range if air resistance is present?

Accepted Answer

The range decreases.

Question 18

Which equation gives the horizontal position $ x $ of a projectile at time $ t $ if the initial horizontal velocity is $ v_{0x} $?

Accepted Answer

$x = v_{0x} t$

Question 19

Which of the following best describes Newton's First Law?

Accepted Answer

An object remains at rest or in uniform motion unless acted upon by a net external force.

Vectors, Kinematics, and Forces in Physics: Study Notes

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