Q: A projectile is launched at an angle $$\theta_i$$ with initial speed $$v_i. $$Which equation gives the range $$R of $$the projectile (assuming it lands at the same height it was launched)?

$$R = \dfrac{v_i^2$ \sin 2\theta_i}{g}$$

Q: A ball is thrown with a velocity of $$10\ \mathrm{m/s} at an $$angle of $$45^\circ. $$What is the equation for its trajectory $$y(x)$$?

$$y(x) = (\tan 45^\circ)x - \dfrac{g}{2(v_i \cos 45^\$$circ)^2$$}x^2$

Question 1

A soccer ball is kicked with an initial speed of $$20\ \mathrm{m/s} at an $$angle of $$30^\circ$$ above the horizontal. What is the maximum height reached by the ball? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$5.1\ \mathrm{m}$$

Question 2

A car accelerates uniformly from rest to a speed of $$30\ \mathrm{m/s} in$$ $$10\ \mathrm{s}. $$What is the car's acceleration?

Accepted Answer

$$1.5\ \mathrm{m/s^2$}$$

Question 3

A projectile is launched at an angle $$	heta_i$$ with initial speed $$v_i. $$Which equation gives the range $$R of $$the projectile (assuming it lands at the same height it was launched)?

Accepted Answer

$$R = \dfrac{v_i^2$ \sin 2	heta_i}{g}$$

Question 4

A cyclist travels $$40\ \mathrm{km}$$ north and then $$30\ \mathrm{km}$$ east. What is the magnitude of the cyclist's displacement?

Accepted Answer

$$50\ \mathrm{km}$$

Question 5

A stone is thrown horizontally from a $$45\ \mathrm{m}$$ high cliff with a speed of $$10\ \mathrm{m/s}. $$How far from the base of the cliff does the stone land? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$21.5\ \mathrm{m}$$

Question 6

A ball is thrown straight up with an initial velocity of $$15\ \mathrm{m/s}. $$How long does it take to reach its maximum height?

Accepted Answer

$$1.53\ \mathrm{s}$$

Question 7

A car moves in a circle of radius $$50\ \mathrm{m} at a $$constant speed of $$20\ \mathrm{m/s}. $$What is the magnitude of its centripetal acceleration?

Accepted Answer

$$8.0\ \mathrm{m/s^2$}$$

Question 8

A vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$5$$

Question 9

A runner accelerates from $$5\ \mathrm{m/s} to$$ $$7\ \mathrm{m/s} in$$ $$4\ \mathrm{s}. $$What is the runner's average acceleration?

Accepted Answer

$$0.25\ \mathrm{m/s^2$}$$

Question 10

A projectile is launched at $$20\ \mathrm{m/s} at an $$angle of $$45^\circ. $$What is the time of flight until it lands? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$4.08\ \mathrm{s}$$

Question 11

A ball is thrown horizontally from a $$20\ \mathrm{m}$$ high building. How long does it take to hit the ground? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$2.02\ \mathrm{s}$$

Question 12

A car travels $$100\ \mathrm{m} in$$ $$5\ \mathrm{s}$$, then $$200\ \mathrm{m} in$$ $$10\ \mathrm{s}. $$What is the car's average velocity for the entire trip?

Accepted Answer

$$10\ \mathrm{m/s}$$

Question 13

A rock is dropped from rest from a height $$h. $$Which equation gives the time $$t it $$takes to reach the ground?

Accepted Answer

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

Question 14

A plane flying horizontally at $$100\ \mathrm{m/s}$$ drops a package from a height of $$490\ \mathrm{m}. $$How far from the point directly below the drop does the package land? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$1000\ \mathrm{m}$$

Question 15

A vector $$\vec{B}$$ has a magnitude of $$10$$ and makes an angle of $$60^\circ$$ with the x-axis. What is the x-component $$B_x$$?

Accepted Answer

$$8.66$$

Question 16

A ball is thrown at $$15\ \mathrm{m/s} at an $$angle of $$60^\circ$$ above the horizontal. What is the initial vertical component of its velocity?

Accepted Answer

$$12.99\ \mathrm{m/s}$$

Question 17

A train moves at a constant speed of $$36\ \mathrm{km/h}$$ around a circular track of radius $$300\ \mathrm{m}. $$What is the magnitude of its centripetal acceleration?

Accepted Answer

$$0.4\ \mathrm{m/s^2$}$$

Question 18

A projectile is launched at $$25\ \mathrm{m/s} at an $$angle $$	heta_i. If $$the range is $$50\ \mathrm{m}$$, what is $$\sin 2	heta_i$$? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$0.784$$

Question 19

A ball is thrown with a velocity of $$10\ \mathrm{m/s} at an $$angle of $$45^\circ. $$What is the equation for its trajectory $$y(x)$$?

Accepted Answer

$$y(x) = (	an 45^\circ)x - \dfrac{g}{2(v_i \cos 45^\$$circ)^2$$}x^2$

Question 20

A car travels around a circular track of radius $$100\ \mathrm{m} at a $$speed of $$20\ \mathrm{m/s}. $$What is the frequency of revolution?

Accepted Answer

$$0.032\ \mathrm{rev/s}$$

Physics Equation Sheet: Kinematics, Vectors, and Projectile Motion

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