Q: A ball is launched from the ground at an angle $$\theta$$ above the horizontal with an initial speed $$v_0. $$Which of the following correctly gives the initial velocity components?

$$v_{0x} = v_0$ \cos \theta$$, $$v_{0y} = v_0$ \sin \theta$$

Q: Which equation correctly gives the time of flight $$T$$ for a projectile launched from ground level with initial speed $$v_0 at $$angle $$\theta$$ above the horizontal?

$$T = \dfrac{2 v_0$ \sin \theta}{g}$$

Q: A projectile is launched with initial velocity $$v_0 at $$angle $$\theta. $$What is the maximum height $$H$$ reached by the projectile?

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

Question 1

A ball is launched from the ground at an angle $$	heta$$ above the horizontal with an initial speed $$v_0. $$Which of the following correctly gives the initial velocity components?

Accepted Answer

$$v_{0x} = v_0$ \cos 	heta$$, $$v_{0y} = v_0$ \sin 	heta$$

Question 2

Which of the following statements about projectile motion (neglecting air resistance) is correct?

Accepted Answer

The horizontal acceleration is zero.

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 car rounds a curve of radius $$r at $$constant speed $$v. $$Which of the following best describes the direction of its acceleration?

Accepted Answer

Radially inward toward the center of the curve

Question 5

A projectile is launched at $$30^\circ$$ and $$60^\circ$$ with the same initial speed $$v_0. $$Which statement is true about their ranges (horizontal distances traveled)?

Accepted Answer

Both have the same range.

Question 6

Which equation correctly gives the time of flight $$T$$ for a projectile launched from ground level with initial speed $$v_0 at $$angle $$	heta$$ above the horizontal?

Accepted Answer

$$T = \dfrac{2 v_0$ \sin 	heta}{g}$$

Question 7

A vector $$\vec{B} is $$multiplied by a scalar $$n = -2. $$What happens to the direction and magnitude of the resulting vector?

Accepted Answer

The magnitude is doubled and the direction is reversed.

Question 8

A ball is thrown horizontally from a cliff with speed $$v_0. $$Which equation gives the time $$t it $$takes to hit the ground from height $$h$$?

Accepted Answer

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

Question 9

Which of the following best describes the difference between a scalar and a vector?

Accepted Answer

A vector has magnitude and direction; a scalar has only magnitude.

Question 10

A rescue plane drops a package while flying horizontally at speed $$v_0 at $$height $$h. $$Neglecting air resistance, where will the package land relative to the plane?

Accepted Answer

Directly below the plane if the plane maintains constant speed

Question 11

Given two vectors $$\vec{A}$$ and $$\vec{B}$$, which graphical method can be used to find their sum?

Accepted Answer

Tip-to-tail rule

Question 12

A projectile is launched with initial velocity $$v_0 at $$angle $$	heta. $$What is the maximum height $$H$$ reached by the projectile?

Accepted Answer

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

Question 13

Which of the following is the correct kinematic equation for the $$x-$$component of position for constant acceleration?

Accepted Answer

$$x_f = x_i + (v_{x})_i \Delta t + \dfrac{1}{2} a_x \Delta t^2$

Question 14

A vector $$\vec{D}$$ has components $$D_x = -6$$ and $$D_y = 8. $$What is the angle $$\phi ($$measured counterclockwise from the positive $$x-$$axis) of $$\vec{D}$$?

Accepted Answer

$$\phi = \arctan\left(\dfrac{8}{-6}\right)$$, which is in the second quadrant

Question 15

A cyclist rides east for 3 km, then north for 4 km. What is the magnitude of the displacement vector from the starting point?

Accepted Answer

$$5 km$$

Question 16

Which of the following is true about the acceleration of an object in uniform circular motion?

Accepted Answer

It is directed radially inward and has constant magnitude.

Question 17

A soccer ball is kicked at $$20 m/s at an $$angle of $$45^\circ$$ above the horizontal. What is the horizontal component of its initial velocity?

Accepted Answer

$$20 \cos 45^\circ$$

Question 18

A vector $$\vec{A} is $$subtracted from vector $$\vec{C} to $$give $$\vec{E} = \vec{C} - \vec{A}. $$Which graphical method can be used to represent this operation?

Accepted Answer

Add $$-\vec{A} to$$ $$\vec{C}$$ using the tip-to-tail method

Question 19

A stone is thrown horizontally from a 45 m high cliff. How long does it take to reach the ground? (Use $$g = 9.8 m/s$^2.)$$

Accepted Answer

$$t = \sqrt{\dfrac{2 	imes 45}{9.8}} \approx 3.03 s$$

Vectors and Motion in Two Dimensions: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards