Q: Which equation correctly describes the vertical position $$y of a $$projectile as a function of horizontal position $$x ($$assuming $$y_0 = 0$ and x_0$ = 0$$)?

$$y = x \tan \$$theta_0$$ - \dfrac{g x^2$}{2 v_0$^2 \cos^2$ \$$theta_0$$}$$

Question 1

Which of the following quantities is a vector?

Accepted Answer

Displacement

Question 2

A hiker walks 8 km east and then 6 km west. What is the magnitude of the resultant displacement?

Accepted Answer

$$2\ \mathrm{km}$$

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 ball is thrown horizontally from a cliff with an initial velocity $$v_{x0}. $$Which of the following statements is true about its motion?

Accepted Answer

The vertical velocity increases linearly with time due to gravity.

Question 5

A projectile is launched with an initial speed $$v_0 at an $$angle $$\$$theta_0$$ above the horizontal. What is the time to reach the maximum height?

Accepted Answer

$$t = \dfrac{v_0$ \sin \$$theta_0$$}{g}$$

Question 6

Which method is NOT a correct way to add two vectors graphically?

Accepted Answer

Placing both vectors tail-to-tail and connecting their heads

Question 7

A river flows east at $$3\ \mathrm{m/s}. A $$boat heads north at $$4\ \mathrm{m/s}$$ relative to the water. What is the boat's speed relative to the shore?

Accepted Answer

$$5\ \mathrm{m/s}$$

Question 8

If a vector $$\vec{V} is $$multiplied by a negative scalar $$-2$$, what happens to the resulting vector?

Accepted Answer

It has twice the magnitude and points in the opposite direction.

Question 9

A soccer ball is kicked from the ground at $$20\ \mathrm{m/s} at an $$angle of $$30^\circ$$ above the horizontal. What is the initial vertical component of velocity?

Accepted Answer

$$20 \sin 30^\circ = 10\ \mathrm{m/s}$$

Question 10

Which equation correctly describes the vertical position $$y of a $$projectile as a function of horizontal position $$x ($$assuming $$y_0 = 0$ and x_0$ = 0$$)?

Accepted Answer

$$y = x 	an \$$theta_0$$ - \dfrac{g x^2$}{2 v_0$^2 \cos^2$ \$$theta_0$$}$$

Question 11

A rescue plane drops a package while flying horizontally at $$60\ \mathrm{m/s}$$ and $$180\ \mathrm{m}$$ above the ground. Neglecting air resistance, how far from the release point does the package land?

Accepted Answer

$$360\ \mathrm{m}$$

Question 12

Which of the following best describes the path of a projectile under the influence of gravity (neglecting air resistance)?

Accepted Answer

A parabola

Question 13

A car travels 5 km north, then 12 km east. What is the magnitude of its displacement?

Accepted Answer

$$13\ \mathrm{km}$$

Question 14

Which of the following is NOT a scalar quantity?

Accepted Answer

Force

Question 15

A ball is thrown with velocity $$v_0 at an $$angle $$\$$theta_0$$ above the horizontal. What is the total time of flight if it lands at the same height it was launched?

Accepted Answer

$$t = \dfrac{2 v_0$ \sin \$$theta_0$$}{g}$$

Question 16

A cyclist rides 10 km east, then 10 km north. What is the direction of the resultant displacement from the starting point?

Accepted Answer

$$45^\circ$$ north of east

Question 17

A swimmer can swim at $$2\ \mathrm{m/s} in $$still water. If she swims directly across a river flowing at $$1.5\ \mathrm{m/s}$$, what is her velocity relative to the shore?

Accepted Answer

$$\sqrt{2^2$ + 1.5^2$} = 2.5\ \mathrm{m/s}$$

Kinematics in Two Dimensions and Vectors: Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard