Q: A projectile is launched with an initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. Neglecting air resistance, what is the time of flight until it returns to the same vertical level?

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

Q: A snowball rolls off a roof sloped at $$40^\circ$$ with a speed of $$7.00\ \mathrm{m/s}$$ from a height of $$14.0\ \mathrm{m}. $$What is the horizontal distance from the edge where it lands? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

$$d = 7.00 \times \sqrt{\dfrac{2 \times 14.0}{9.8}}$$

Q: A daring swimmer leaps horizontally from a cliff $$9.50\ \mathrm{m}$$ above the water, aiming to clear a ledge $$1.50\ \mathrm{m}$$ wide. What is the minimum horizontal speed required to clear the ledge?

$$v_{min} = \dfrac{1.50}{\sqrt{2 \times 9.50 / 9.8}}$$

Question 1

A ball is launched from ground level with an initial velocity $$\vec{v}_0 at an $$angle $$	heta$$ above the horizontal. Which of the following correctly describes the horizontal and vertical components of the ball's velocity at the peak of its trajectory?

Accepted Answer

The horizontal component is constant and nonzero, and the vertical component is zero.

Question 2

A projectile is launched with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. Neglecting air resistance, what is the time of flight until it returns to the same vertical level?

Accepted Answer

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

Question 3

Which of the following statements about projectile motion is correct?

Accepted Answer

The horizontal velocity remains constant throughout the flight.

Question 4

A ball is thrown horizontally from a cliff and another is dropped from the same height at the same time. Which statement is true about their times to reach the ground?

Accepted Answer

Both balls reach the ground at the same time.

Question 5

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What launch angle maximizes the range over level ground?

Accepted Answer

$$45^\circ$$

Question 6

A human cannonball is launched and follows a parabolic trajectory. At which point(s) is the vertical component of velocity zero?

Accepted Answer

At the peak of the trajectory.

Question 7

A pendulum swings from position 1 to position 3 as shown. At position 2 (the lowest point), what is the direction of the acceleration vector?

Accepted Answer

Radially inward toward the pivot.

Question 8

An airplane wishes to fly due west, but a wind blows due south. If the plane's airspeed is $$v_{PA}$$ and the wind speed is $$v_{AG}$$, what direction should the pilot head relative to west?

Accepted Answer

$$\arctan\left(\dfrac{v_{AG}}{v_{PA}}\right)$$ north of west

Question 9

A snowball rolls off a roof sloped at $$40^\circ$$ with a speed of $$7.00\ \mathrm{m/s}$$ from a height of $$14.0\ \mathrm{m}. $$What is the horizontal distance from the edge where it lands? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$d = 7.00 	imes \sqrt{\dfrac{2 	imes 14.0}{9.8}}$$

Question 10

A daring swimmer leaps horizontally from a cliff $$9.50\ \mathrm{m}$$ above the water, aiming to clear a ledge $$1.50\ \mathrm{m}$$ wide. What is the minimum horizontal speed required to clear the ledge?

Accepted Answer

$$v_{min} = \dfrac{1.50}{\sqrt{2 	imes 9.50 / 9.8}}$$

Question 11

Which of the following changes would increase the range of a projectile launched over level ground?

Accepted Answer

Reducing the launch angle from $$60^\circ to$$ $$45^\circ.$$

Question 12

In two-dimensional motion, what information do you need to find the speed of an object at any point of its path?

Accepted Answer

The coordinates of the object as functions of time.

Question 13

For a projectile launched horizontally, which of the following best describes the horizontal component of its velocity? Assume air resistance is negligible.

Accepted Answer

It remains a nonzero constant.

Question 14

A ball is launched with initial velocity components $$v_{0x} = 15.0\ \mathrm{m/s}$$ and $$v_{0y} = 26.0\ \mathrm{m/s}. $$What is the magnitude of the initial velocity?

Accepted Answer

$$\sqrt{(15.0)^2$ + (26.0)^2$}$$

Question 15

At the peak of a projectile's trajectory, what is the direction of the acceleration vector?

Accepted Answer

Downward

Question 16

A particle is at rest at the corner of a cube-shaped box with dimensions $$2\ \mathrm{m} 	imes 2\ \mathrm{m} 	imes 2\ \mathrm{m} at $$time $$t = 2\ \mathrm{s}. $$What are the Cartesian coordinates of the particle if the origin is at one corner?

Accepted Answer

$$(2, 2, 2)$$

Motion in Two or Three Dimensions: Projectile Motion, Relative Velocity, and Pendulum Dynamics

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