Q: A projectile is launched from the ground at an angle $$\theta$$ above the horizontal with initial speed $$v_0. $$Which of the following correctly gives the time of flight until it returns to the ground?

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

Q: A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. What is the formula for its maximum height?

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

Q: A spacecraft has velocity components $$v_x = 22\ \mathrm{m/s}$$ and $$v_y = 14\ \mathrm{m/s}. $$What is the angle $$\theta$$ between its velocity vector and the $$+x-$$axis?

$$\theta = \tan$$^{-1}$$\left(\dfrac{14}{22}\right) \approx 32.5^\circ$$

Question 1

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

Accepted Answer

$$\approx 30\ \mathrm{m}$$

Question 2

A projectile is launched from the ground at an angle $$	heta$$ above the horizontal with initial speed $$v_0. $$Which of the following correctly gives the time of flight until it returns to the ground?

Accepted Answer

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

Question 3

A rescue plane flying horizontally at $$60\ \mathrm{m/s} at a $$height of $$180\ \mathrm{m}$$ drops a package. How far horizontally from the drop point does the package land? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\approx 360\ \mathrm{m}$$

Question 4

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

Accepted Answer

The horizontal velocity remains constant while the vertical velocity changes due to gravity.

Question 5

A vector $$\vec{A}$$ has a magnitude of $$15\ \mathrm{N}$$ and points $$67^\circ$$ above the $$+x-$$axis. What are its $$x$$ and $$y$$ components?

Accepted Answer

$$A_x = 6\ \mathrm{N},\ A_y = 14\ \mathrm{N}$$

Question 6

A ball is thrown directly upward with an initial velocity of $$20\ \mathrm{m/s}. $$What is the maximum height it reaches? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\approx 20.4\ \mathrm{m}$$

Question 7

A bird flies $$0.619\ \mathrm{km}$$ due east and then $$0.470\ \mathrm{km} in a $$direction $$61.2^\circ$$ north of west. What is the magnitude of its total displacement?

Accepted Answer

$$\approx 0.84\ \mathrm{km}$$

Question 8

A train moves east at $$34.6\ \mathrm{m/s}$$ and another train moves west at $$20.7\ \mathrm{m/s}. $$What is the velocity of the first train as seen by a passenger on the second train?

Accepted Answer

$$55.3\ \mathrm{m/s}$$\ east

Question 9

A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the formula for its maximum height?

Accepted Answer

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

Question 10

A dolphin swims at $$5.62\ \mathrm{m/s} at an $$angle of $$49.8^\circ$$ above the horizontal. What is the vertical component of its velocity?

Accepted Answer

$$\approx 4.29\ \mathrm{m/s}$$

Question 11

Which equation gives the magnitude of the velocity vector $$\vec{v} in $$two dimensions, given its components $$v_x$$ and $$v_y$$?

Accepted Answer

$$|\vec{v}| = \sqrt{v_x^2$ + v_y^2$}$$

Question 12

A soccer ball is kicked with an initial velocity of $$20\ \mathrm{m/s} at an $$angle of $$30^\circ$$ above the horizontal. What is the range of the ball? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\approx 35.3\ \mathrm{m}$$

Question 13

A package is dropped from a plane flying horizontally at $$100\ \mathrm{m/s} at a $$height of $$500\ \mathrm{m}. $$How long does it take to reach the ground? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\approx 7.14\ \mathrm{s}$$

Question 14

Which of the following best describes the direction of acceleration for a ball thrown straight up (neglecting air resistance)?

Accepted Answer

Downward during the entire time the ball is in the air.

Question 15

A boat moves at $$7.0\ \mathrm{m/s}$$ relative to the water. A passenger walks toward the back of the boat at $$2.0\ \mathrm{m/s}$$ relative to the boat. What is the passenger's velocity relative to the water?

Accepted Answer

$$5.0\ \mathrm{m/s}$$\ forward

Question 16

A spacecraft has velocity components $$v_x = 22\ \mathrm{m/s}$$ and $$v_y = 14\ \mathrm{m/s}. $$What is the angle $$	heta$$ between its velocity vector and the $$+x-$$axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$\left(\dfrac{14}{22}ight) \approx 32.5^\circ$$

Question 17

Which kinematic equation gives the $$y-$$component of displacement for constant acceleration?

Accepted Answer

$$y = v_{0y} t + \dfrac{1}{2} a_y t^2$

Kinematics in Two Dimensions: Concepts, Equations, and Projectile Motion

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