Q: Which equation correctly gives the range $$R of a $$projectile launched at speed $$v_0$$ and angle $$\theta ($$assuming symmetric trajectory and no air resistance)?

$$R = \dfrac{v_0$^2 \sin2\theta}{g}$$

Q: A ball is thrown with initial velocity $$v_0 at $$angle $$\theta. $$Which pair of angles will result in the same range, assuming symmetric trajectory and no air resistance?

$$\theta$$ and $$90^\circ - \theta$$

Question 1

A soccer ball is kicked from ground level with an initial velocity of $$v_0 = 20$$\ \mathrm{m/s}$$ at an angle of 30$$^\circ$$ above the horizontal. Neglecting air resistance, what is the maximum height reached by the ball?

Accepted Answer

$$h_{max} = \dfrac{(20\sin30^\$$circ)^2$$}{2g}$$

Question 2

Which of the following statements about average velocity in two-dimensional motion is correct?

Accepted Answer

Average velocity is independent of the path taken and depends only on displacement.

Question 3

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

Accepted Answer

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

Question 4

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$For which angle is the range maximized, assuming symmetric trajectory and no air resistance?

Accepted Answer

$$	heta = 45^\circ$$

Question 5

A car moves east at $$20\ \mathrm{m/s} on a $$moving walkway that travels east at $$5\ \mathrm{m/s}. $$What is the car's velocity relative to a stationary observer?

Accepted Answer

$$25\ \mathrm{m/s}$$\ east

Question 6

Which of the following correctly expresses the position vector $$\vec{r} of a $$particle moving in the $$xy-$$plane under constant acceleration?

Accepted Answer

$$\vec{r} = \vec{r}_0 + \vec{v}_0 t + \dfrac{1}{2}\vec{a}t^2$

Question 7

A ball is thrown horizontally from a cliff with speed $$v_0. $$Which statement about its motion is correct (neglecting air resistance)?

Accepted Answer

The horizontal velocity remains constant while the vertical velocity increases linearly with time.

Question 8

A cyclist moves north at $$10\ \mathrm{m/s}$$ while a wind blows east at $$5\ \mathrm{m/s}. $$What is the magnitude of the cyclist's velocity relative to the ground?

Accepted Answer

$$\sqrt{10^2$ + 5^2$} = 11.18\ \mathrm{m/s}$$

Question 9

Which of the following is true about the acceleration of a projectile at the highest point of its trajectory (neglecting air resistance)?

Accepted Answer

The acceleration is directed downward and equals $$g.$$

Question 10

A train moves at $$30\ \mathrm{m/s}$$ east. A passenger walks at $$2\ \mathrm{m/s}$$ west inside the train. What is the passenger's velocity relative to the ground?

Accepted Answer

$$28\ \mathrm{m/s}$$\ east

Question 11

Which equation correctly gives the range $$R of a $$projectile launched at speed $$v_0$$ and angle $$	heta ($$assuming symmetric trajectory and no air resistance)?

Accepted Answer

$$R = \dfrac{v_0$^2 \sin2	heta}{g}$$

Question 12

In uniform circular motion, what is the direction of the centripetal acceleration vector?

Accepted Answer

Toward the center of the circle

Question 13

A stone is thrown at $$v_0 = 15$$\ \mathrm{m/s}$$ at 60$$^\circ$$ above the horizontal. What is the initial vertical component of velocity?

Accepted Answer

$$v_{0y} = 15\sin60^\circ$$

Question 14

Which of the following best describes the instantaneous velocity vector at any point along a curved path?

Accepted Answer

It is tangent to the path at that point and in the direction of motion.

Question 15

A ball is thrown with initial velocity $$v_0 at $$angle $$	heta. $$Which pair of angles will result in the same range, assuming symmetric trajectory and no air resistance?

Accepted Answer

$$	heta$$ and $$90^\circ - 	heta$$

Question 16

Which of the following is a correct statement about the independence of motion in two dimensions?

Accepted Answer

Motion in the $$x$$ and $$y$$ directions can be analyzed independently.

Question 17

A runner moves at $$6\ \mathrm{m/s}$$ north on a moving walkway going $$2\ \mathrm{m/s}$$ south. What is the runner's velocity relative to the ground?

Accepted Answer

$$4\ \mathrm{m/s}$$\ north

Question 18

Which of the following is the correct expression for instantaneous acceleration?

Accepted Answer

$$a = \dfrac{dv}{dt}$$

Question 19

A car travels in a circle of radius $$10\ \mathrm{m} at a $$speed of $$5\ \mathrm{m/s}. $$What is the period $$T of $$one revolution?

Accepted Answer

$$T = \dfrac{2\pi 	imes 10}{5}$$

(CH3) Kinematics in Two Dimensions: Position, Velocity, and Acceleration

Guida di studio - Domande di pratica

Study guide - Flashcard