Q: A projectile is launched with an initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. Which equation gives the range of the projectile?

$$x = \dfrac{v_0$^2 \sin(2\theta)}{g}$$

Question 1

A ball is thrown horizontally from the top of a 45 m high building with an initial speed of 10 m/s. Neglecting air resistance, how far from the base of the building will the ball land? Use $$g = 9.8\ m/s^2$.

Accepted Answer

$$30.3\ m$$

Question 2

Which equation correctly expresses the gravitational force between two masses $$m_1$$ and $$m_2$$ separated by a distance $$r$$?

Accepted Answer

$$F_g = G \dfrac{m_1$ m_2$}{r^2$}$$

Question 3

A car accelerates from rest at a constant rate of $$2\ m/s^2$ for 5$ seconds. What is its final velocity?

Accepted Answer

$$10\ m/s$$

Question 4

A projectile is launched with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. Which equation gives the range of the projectile?

Accepted Answer

$$x = \dfrac{v_0$^2 \sin(2	heta)}{g}$$

Question 5

A block slides down a frictionless incline of height $$h. $$What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 6

A 5 kg object is acted upon by a net force of 20 N. What is its acceleration?

Accepted Answer

$$4\ m/s^2$

Question 7

Which of the following is the correct expression for the maximum static friction force?

Accepted Answer

$$f_{s,max} = \mu_s F_N$$

Question 8

A satellite orbits Earth in a circular path of radius $$r$$ with speed $$v. $$What is the centripetal acceleration?

Accepted Answer

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

Question 9

A wheel completes 120 revolutions in 2 minutes. What is its frequency?

Accepted Answer

$$1	ext{ rev/s}$$

Question 10

A right triangle has legs of length 3 and 4 units. What is the length of the hypotenuse?

Accepted Answer

$$5$$

Question 11

A ball is thrown upward with initial velocity $$v_i = 20\ m/s. $$How long does it take to reach its maximum height? (Use $$g = 9.8\ m/s^2$)

Accepted Answer

$$2.04\ s$$

Question 12

Which formula would you use to find the area of a sphere?

Accepted Answer

$$A_{sphere} = 4\pi r^2$

Question 13

A car travels from $$x_i = 0 m to$$ $$x_f = 100 m in$$ $$t_f - t_i = 20 s. $$What is its average velocity?

Accepted Answer

$$5\ m/s$$

Question 14

If $$0 = ax^2$ + bx + c$$, what is the solution for $$x$$?

Accepted Answer

$$x = \dfrac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 15

A cyclist moves at a constant speed of $$12\ m/s$$ around a circular track of radius $$30\ m. $$What is the period of one revolution?

Accepted Answer

$$T = \dfrac{2\pi r}{v}$$

Question 16

A block of mass $$m is $$pulled across a horizontal surface with kinetic friction coefficient $$\mu_k. $$What is the force of kinetic friction?

Accepted Answer

$$f_k = \mu_k F_N$$

Question 17

A ball rolls off a table with horizontal velocity $$v_{i,x}. $$Which equation gives its horizontal position after time $$t$$?

Accepted Answer

$$x = x_i + v_{i,x} t$$

Question 18

A right triangle has an angle $$	heta$$ such that $$\sin	heta = 0.6. $$What is the ratio of the opposite side to the hypotenuse?

Accepted Answer

$$0.6$$

Question 19

A car starts from rest and accelerates at $$3\ m/s^2$ for 4$ seconds. What distance does it cover?

Accepted Answer

$$16\ m$$

Physics 2025 Exam 1 Formula Sheet: Essential Equations and Concepts

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