Q: Which equation correctly relates the angle $$\theta of a $$vector to its components?

$$\tan \theta = \frac{V_y}{V_x}$$

Question 1

Which of the following quantities is a vector?

Accepted Answer

Displacement

Question 2

A car travels 8 km east, then 6 km east. What is the resultant displacement?

Accepted Answer

$$14\ 	ext{km}$$ east

Question 3

A vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$5$$

Question 4

A projectile is launched horizontally from a $$50.0\ 	ext{m}$$ high cliff and lands $$90.0\ 	ext{m}$$ from the base. What was its initial speed?

Accepted Answer

$$14.2\ 	ext{m/s}$$

Question 5

A football is kicked at $$20.0\ 	ext{m/s} at an $$angle of $$37.0^\circ$$ above the horizontal. What is the maximum height reached?

Accepted Answer

$$6.9\ 	ext{m}$$

Question 6

A boat can move at $$1.85\ 	ext{m/s} in $$still water. If the river flows west at $$1.20\ 	ext{m/s}$$, at what angle upstream should the boat head to go directly north?

Accepted Answer

$$\arcsin\left(\frac{1.20}{1.85}\right) = 40.5^\circ$$ west of north

Question 7

A tiger leaps horizontally from a $$7.5\ 	ext{m}$$ high rock with a speed of $$3\ 	ext{m/s}. $$How far from the base will she land?

Accepted Answer

$$3.7\ 	ext{m}$$

Question 8

Which equation correctly relates the angle $$	heta of a $$vector to its components?

Accepted Answer

$$	an 	heta = \frac{V_y}{V_x}$$

Question 9

A projectile is fired with an initial speed of $$36.6\ 	ext{m/s} at$$ $$42.2^\circ$$ above the horizontal. What is the total time in the air?

Accepted Answer

$$4.98\ 	ext{s}$$

Question 10

A vector $$\vec{V} is $$multiplied by a negative scalar $$-2. $$What is the direction and magnitude of the resulting vector?

Accepted Answer

Opposite direction, twice the magnitude

Question 11

A diver runs at $$2.5\ 	ext{m/s}$$ and dives horizontally from a cliff, hitting the water $$3.0\ 	ext{s}$$ later. How high is the cliff?

Accepted Answer

$$44.1\ 	ext{m}$$

Question 12

A rural mail carrier drives $$22.0\ 	ext{km}$$ north, then $$47.0\ 	ext{km} at$$ $$60.0^\circ$$ south of east. What is the magnitude of her displacement from the post office?

Accepted Answer

$$49.6\ 	ext{km}$$

Question 13

Which of the following best describes projectile motion near Earth's surface (ignoring air resistance)?

Accepted Answer

The horizontal velocity is constant and the vertical velocity changes due to gravity.

Question 14

A cannon fires a projectile at $$60.0\ 	ext{m/s} to $$hit a target $$320\ 	ext{m}$$ away. At what angle should it be fired?

Accepted Answer

$$15.6^\circ$$

Question 15

A boat heads directly across a $$110\ 	ext{m}$$ wide river at $$1.85\ 	ext{m/s}$$, while the current is $$1.20\ 	ext{m/s}$$ west. How long does it take to cross?

Accepted Answer

$$59.5\ 	ext{s}$$

Question 16

Which of the following is the correct equation for the range $$R of a $$projectile launched at speed $$v_0$$ and angle $$\$$theta_0$$ from the ground?

Accepted Answer

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

Question 17

If a vector $$\vec{A} is $$subtracted from $$\vec{B}$$, which graphical method is correct?

Accepted Answer

Add $$\vec{B}$$ and $$-\vec{A}$$ tail-to-tip

Question 18

A projectile is launched at an angle $$\$$theta_0$$ with initial speed v_0$. What is the vertical component of the initial velocity?

Accepted Answer

$$v_0$$ \sin \$$theta_0$$

Question 19

A plane flies $$620\ 	ext{km}$$ east, then $$440\ 	ext{km}$$ southeast ($$45^\circ$$), then $$550\ 	ext{km} at$$ $$53^\circ$$ south of west. What is the best method to find the total displacement?

Accepted Answer

Add the vectors graphically using the tail-to-tip method and resolve into components.

Kinematics in Two Dimensions and Vectors: Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard