Q: A projectile is launched from ground level with an initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. Neglecting air resistance, what is the formula for the maximum range $$R of $$the projectile over level ground?

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

Q: A particle moves in a plane with velocity components $$v_x$$ and $$v_y. $$What is the direction $$\theta of $$the velocity vector with respect to the positive $$x-$$axis?

$$\theta = \tan$$^{-1}$$\left(\dfrac{v_y}{v_x}\right)$$

Question 1

A projectile is launched from ground level with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. Neglecting air resistance, what is the formula for the maximum range $$R of $$the projectile over level ground?

Accepted Answer

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

Question 2

A ball is thrown horizontally from a cliff of height $$h$$ with initial speed $$v_0. $$How long does it take to hit the ground?

Accepted Answer

$$t = \sqrt{\dfrac{2h}{g}}$$

Question 3

A car drives off a $$10.0\ \mathrm{m}$$ high cliff at $$20.0\ \mathrm{m/s}$$ horizontally. How far from the base of the cliff does it land? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$x = 28.6\ \mathrm{m}$$

Question 4

Two balls of equal mass are released from the same height above the ground at the same instant. One is dropped vertically, the other is projected horizontally. Neglecting air resistance, which hits the ground first?

Accepted Answer

They hit at the same time.

Question 5

A hunter aims directly at a coconut hanging from a tree. At the instant the arrow is released, the coconut falls. Will the arrow hit the coconut (neglecting air resistance)?

Accepted Answer

Yes, the arrow will hit the coconut.

Question 6

A particle moves in a plane with velocity components $$v_x$$ and $$v_y. $$What is the direction $$	heta of $$the velocity vector with respect to the positive $$x-$$axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$\left(\dfrac{v_y}{v_x}ight)$$

Question 7

A ball 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 8

Sofia and Rasheed are riding a merry-go-round spinning steadily. Sofia is twice as far from the axis as Rasheed. How does Sofia's tangential velocity compare to Rasheed's?

Accepted Answer

Sofia's tangential velocity is twice Rasheed's.

Question 9

Sofia and Rasheed are riding a merry-go-round spinning steadily. Sofia is twice as far from the axis as Rasheed. How does Sofia's centripetal acceleration compare to Rasheed's?

Accepted Answer

Sofia's centripetal acceleration is four times Rasheed's.

Question 10

A mouse runs straight across a conveyor belt moving at $$3\ \mathrm{m/s}$$, heading for cheese at $$4\ \mathrm{m/s}$$ relative to the belt. What is the mouse’s speed relative to the factory floor?

Accepted Answer

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

Question 11

A plane flies due east at $$500\ \mathrm{mph}$$ relative to the air, but the wind blows south at $$50\ \mathrm{mph}. $$What is the plane’s ground speed?

Accepted Answer

$$v = \sqrt{500^2$ + 50^2$}\ \mathrm{mph}$$

Question 12

A ball moves in uniform circular motion with angular velocity $$\omega. $$What is the relationship between its tangential speed $$v$$ and $$\omega$$?

Accepted Answer

$$v = \omega r$$

Question 13

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

Accepted Answer

Acceleration can change the magnitude and/or the direction of velocity.

Question 14

A particle moves from position $$\vec{r}_1 to$$ $$\vec{r}_2 in $$time $$\Delta t. $$What is the formula for its average velocity?

Accepted Answer

$$\vec{v}_{avg} = \dfrac{\vec{r}_2 - \vec{r}_1}{\Delta t}$$

Question 15

A ball rolls around a $$1.0\ \mathrm{m}$$ diameter roulette wheel, completing one revolution in $$2.0\ \mathrm{s}. $$What is its angular velocity?

Accepted Answer

$$\omega = \dfrac{2\pi}{2.0} = 3.14\ \mathrm{rad/s}$$

Question 16

A car is traveling around a circular track at a steady $$45\ \mathrm{mph}. Is $$the car accelerating?

Accepted Answer

Yes, because its direction is changing.

Question 17

A particle moves in a circle of radius $$r$$ with constant angular velocity $$\omega. $$What is the formula for its centripetal acceleration?

Accepted Answer

$$a_c = \$$omega^2$$ r$$

Question 18

Which of the following is true about reference frames in kinematics?

Accepted Answer

Velocity is always measured relative to a chosen reference frame.

Kinematics in Two Dimensions – Physics for Scientists and Engineers (Chapter 4 Study Notes)

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