Q: A boat heads due north across a river with velocity $$10.0 km/h $$relative to the water. The river flows east at $$5.00 km/h. $$What is the boat's velocity relative to an observer on the bank?

$$v = \sqrt{(10.0)^2$ + (5.00)^2$} km/h$\ at\ \theta = \tan$$^{-1}$$(5.00/10.0)$$ east of north

Q: A block of mass $$2.5 kg $$rests on a ramp with a coefficient of static friction $$\mu_s = 0.35. $$What is the maximum angle $$\theta$$ before the block starts to slip?

$$\theta = \tan$$^{-1}$$(0.35)$$

Question 1

Which of the following statements about projectile motion is correct?

Accepted Answer

The x-component of velocity remains constant, while the y-component changes due to gravity.

Question 2

A ball is thrown with an initial velocity $$v_0 at an $$angle $$\$$theta_0$$ above the horizontal. What is the correct expression for the initial y-component of velocity?

Accepted Answer

$$v_{0y} = v_0$ \sin \$$theta_0$$

Question 3

A hiker walks 25.0 km at $$45.0^\circ$$ south of east, then 40.0 km at $$60.0^\circ$$ north of east. What is the correct method to find the total displacement?

Accepted Answer

Add the x- and y-components of each displacement separately, then use the Pythagorean theorem.

Question 4

Which equation gives the range $$R of a $$projectile launched from ground level with initial speed $$v_0 at $$angle $$\$$theta_0$$ (neglecting air resistance)?

Accepted Answer

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

Question 5

A block of mass $$m$$ rests on a ramp inclined at angle $$	heta. $$What is the acceleration of the block down the ramp if friction is neglected?

Accepted Answer

$$a = g \sin 	heta$$

Question 6

Which of the following is a vector quantity?

Accepted Answer

Displacement

Question 7

If a vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4$$, what is its magnitude?

Accepted Answer

$$A = 5$$

Question 8

A rescue plane drops a package from a height of 100 m while flying horizontally at 40 m/s. Neglecting air resistance, how far from the release point does the package land?

Accepted Answer

$$x = v_{0x} t$$,\ where\ t = \sqrt{\frac{2h}{g}}$

Question 9

Which of the following best describes the commutative law of vector addition?

Accepted Answer

$$\vec{A} + \vec{B} = \vec{B} + \vec{A}$$

Question 10

A car moves in a circle of radius $$r at $$constant speed $$v. $$What is the magnitude of its centripetal acceleration?

Accepted Answer

$$a_c = \frac{v^2$}{r}$$

Question 11

A boat heads due north across a river with velocity $$10.0 km/h $$relative to the water. The river flows east at $$5.00 km/h. $$What is the boat's velocity relative to an observer on the bank?

Accepted Answer

$$v = \sqrt{(10.0)^2$ + (5.00)^2$} km/h$\ at\ 	heta = 	an$$^{-1}$$(5.00/10.0)$$ east of north

Question 12

Which of the following is the correct formula for the y-component of a vector $$A at $$angle $$	heta$$ from the x-axis?

Accepted Answer

$$A_y = A \sin 	heta$$

Question 13

A projectile is launched at $$30^\circ$$ and $$60^\circ$$ with the same speed. Which statement is true about their ranges?

Accepted Answer

The ranges are equal.

Question 14

If $$\vec{A} = 5$$ units at $$53^\circ$$ above the x-axis, what are its x- and y-components?

Accepted Answer

$$A_x = 5 \cos 53^\circ$$, $$A_y = 5 \sin 53^\circ$$

Question 15

A block of mass $$2.5 kg $$rests on a ramp with a coefficient of static friction $$\mu_s = 0.35. $$What is the maximum angle $$	heta$$ before the block starts to slip?

Accepted Answer

$$	heta = 	an$$^{-1}$$(0.35)$$

Question 16

Which of the following best describes the negative of a vector $$\vec{A}$$?

Accepted Answer

A vector with the same magnitude as $$\vec{A}$$ but in the opposite direction.

Question 17

Which of the following is the correct formula for the magnitude of the resultant vector $$\vec{R}$$ from components $$R_x$$ and $$R_y$$?

Accepted Answer

$$R = \sqrt{R_x^2$ + R_y^2$}$$

Question 18

A car travels east at 60 km/h and another car travels north at 80 km/h. What is the velocity of the first car relative to the second?

Accepted Answer

$$v = \sqrt{(60)^2$ + (80)^2$} km/h$\ at\ 	heta = 	an$$^{-1}$$(80/60)$$ east of south

Vectors and Motion in Two Dimensions: Structured Study Notes

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