Q: A ball is thrown horizontally from a $$45\ \mathrm{m}$$ high cliff with a speed of $$10\ \mathrm{m/s}. $$How long does it take to hit the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 45}{9.8}} \approx 3.03\ \mathrm{s}$$

Q: A projectile is launched with an initial velocity of $$v_0 at an $$angle $$\theta$$ above the horizontal. Which equation gives the maximum height reached by the projectile?

$$h_{max} = \frac{v_0$^2 \sin^2$ \theta}{2g}$$

Q: A car is moving with velocity components $$v_x = 12\ \mathrm{m/s}$$ and $$v_y = 5\ \mathrm{m/s}. $$What is the direction of the velocity vector with respect to the positive $$x-$$axis?

$$\theta = \tan$$^{-1}$$ \left( \frac{v_y}{v_x} \right ) = \tan$$^{-1}$$ \left( \frac{5}{12} \right ) \approx 22.6^\circ$$

Question 1

A soccer ball is kicked from the ground at an angle of $$30^\circ$$ above the horizontal with an initial speed of $$20\ \mathrm{m/s}. $$Neglecting air resistance, what is the horizontal component of the ball's velocity?

Accepted Answer

$$v_x = 20 \cos 30^\circ = 17.3\ \mathrm{m/s}$$

Question 2

Which of the following best describes the acceleration of a projectile in two-dimensional motion (neglecting air resistance)?

Accepted Answer

The acceleration is constant and points downward with magnitude $$g$$

Question 3

A car rounds a flat circular track of radius $$50\ \mathrm{m} at a $$constant speed of $$20\ \mathrm{m/s}. $$What is the magnitude of its centripetal acceleration?

Accepted Answer

$$a_c = \frac{v^2$}{r} = \frac{(20)^2$}{50} = 8\ \mathrm{m/s^2$}$$

Question 4

A particle moves along a curved path in the $$xy-$$plane. At a certain instant, its velocity components are $$v_x = 3\ \mathrm{m/s}$$ and $$v_y = 4\ \mathrm{m/s}. $$What is the speed of the particle?

Accepted Answer

$$v = \sqrt{v_x^2$ + v_y^2$} = 5\ \mathrm{m/s}$$

Question 5

Which equation correctly relates the velocity of object C in reference frame B, given the velocity of C in frame A and the velocity of A in frame B?

Accepted Answer

$$\vec{v}_{CB} = \vec{v}_{CA} + \vec{v}_{AB}$$

Question 6

A ball is thrown horizontally from a $$45\ \mathrm{m}$$ high cliff with a speed of $$10\ \mathrm{m/s}. $$How long does it take to hit the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 	imes 45}{9.8}} \approx 3.03\ \mathrm{s}$$

Question 7

If the velocity vector of a particle is always tangent to its trajectory, what does this imply about the direction of the instantaneous velocity?

Accepted Answer

The instantaneous velocity is always tangent to the path

Question 8

A projectile is launched with an initial velocity of $$v_0 at an $$angle $$	heta$$ above the horizontal. Which equation gives the maximum height reached by the projectile?

Accepted Answer

$$h_{max} = \frac{v_0$^2 \sin^2$ 	heta}{2g}$$

Question 9

Which of the following statements about centripetal acceleration is correct?

Accepted Answer

Centripetal acceleration always points toward the center of the circle

Question 10

A car is moving with velocity components $$v_x = 12\ \mathrm{m/s}$$ and $$v_y = 5\ \mathrm{m/s}. $$What is the direction of the velocity vector with respect to the positive $$x-$$axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$ \left( \frac{v_y}{v_x} ight ) = 	an$$^{-1}$$ \left( \frac{5}{12} ight ) \approx 22.6^\circ$$

Question 11

Which of the following is a correct expression for the average acceleration vector $$\vec{a}_{avg}$$?

Accepted Answer

$$\vec{a}_{avg} = \frac{\Delta \vec{v}}{\Delta t}$$

Question 12

A cyclist travels east at $$8\ \mathrm{m/s}$$ relative to the ground, while a wind blows north at $$6\ \mathrm{m/s}$$ relative to the ground. What is the magnitude of the cyclist's velocity relative to the air?

Accepted Answer

$$v = \sqrt{8^2$ + 6^2$} = 10\ \mathrm{m/s}$$

Question 13

Which of the following best describes the difference between angular velocity $$\omega$$ and linear velocity $$v$$ for an object in circular motion?

Accepted Answer

$$v = r \omega$$

Question 14

A projectile is launched horizontally from a height $$h$$ with initial speed $$v_0. $$Which equation gives the horizontal distance traveled before hitting the ground?

Accepted Answer

$$x = v_0$ t$$,\ 	ext{where}\ t = \sqrt{\frac{2h}{g}}$

Question 15

Which of the following is NOT a characteristic of projectile motion (neglecting air resistance)?

Accepted Answer

The vertical velocity is constant

Question 16

A ball is thrown at an angle $$	heta$$ with initial speed $$v_0. $$Which equation gives the time of flight until it returns to the same vertical level?

Accepted Answer

$$t = \frac{2 v_0$ \sin 	heta}{g}$$

Kinematics in Two Dimensions: Study Notes

Study Guide - Practice Questions

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