Q: A Frisbee's horizontal coordinates are given by $$x(t) = 3t$$ and $$y(t) = 4t - 5t^2$, where x$ and y$ are in meters and t$ is in seconds. What is the acceleration of the Frisbee? Give a magnitude and a direction, measuring angles from the positive x$ direction.

$$10\ \text{m/s}^2$$, $$323^{\circ}$

Q: A projectile is fired from a cliff with initial velocity components $$v_{0x} = 60.0\ \text{m/s}$$ and $$v_{0y} = 80.0\ \text{m/s}. $$What is the vertical velocity component after $$21.0\ \text{s}$$?

$$v_y = 80.0 - 9.8 \times 21.0$$

Q: A projectile is launched from a cliff with initial velocity $$v_0 at $$angle $$ heta$$ above the horizontal. If the projectile lands at distance $$D$$ from the base of the cliff, which equation best describes the horizontal displacement?

$$D = v_0$ \cos\theta \cdot t$$

Q: A projectile is fired from a cliff with initial velocity $$v_0 at $$angle $$ heta. If $$the time of flight is $$T$$, what is the vertical displacement at time $$t$$?

$$y = v_0$ \sin\theta \cdot t - \frac{1}{2} g t^2$

Q: A projectile is launched from a cliff with initial velocity $$v_0 at $$angle $$\theta. If $$the projectile lands at distance $$D$$ from the base, which equation best describes the time of flight?

$$t = \frac{D}{v_0$ \cos\theta}$$

Q: A projectile is fired from a cliff with initial velocity $$v_0 at $$angle $$\theta. If $$the projectile lands at distance $$D$$ from the base, which equation best describes the maximum height reached?

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

Question 1

A projectile is fired from point O at the edge of a cliff with initial velocity components $$v_{0x}$$ and $$v_{0y}$$, as shown in the diagram. If the projectile's time of flight is 40.0 s and it experiences no appreciable air resistance, what is the magnitude of its velocity 21.0 s after it is fired?

Accepted Answer

$$67.4\ 	ext{m/s}$$

Question 2

A hobby rocket reaches a height of $$1.00\ 	ext{km}$$ and lands $$2.00\ 	ext{km}$$ from the launch point with no air resistance. What was the angle of launch?

Accepted Answer

$$69.0^{\circ}$$

Question 3

A child throws a ball with an initial speed of $$6.00\ 	ext{m/s} at an $$angle of $$40.0^{\circ}$$ above the horizontal. The ball leaves her hand $$1.00\ 	ext{m}$$ above the ground and experiences negligible air resistance. How far from where the child is standing does the ball hit the ground?

Accepted Answer

$$7.46\ 	ext{m}$$

Question 4

An airplane is flying at a speed of $$200\ 	ext{km/h} in $$level flight at an altitude of $$500\ 	ext{m}. A $$package is to be dropped from the airplane to land on a target on the ground. Ignore air resistance. At what horizontal distance away from the target should the package be released so that it lands on the target?

Accepted Answer

$$2.56\ 	ext{km}$$

Question 5

A Frisbee's horizontal coordinates are given by $$x(t) = 3t$$ and $$y(t) = 4t - 5t^2$, where x$ and y$ are in meters and t$ is in seconds. What is the acceleration of the Frisbee? Give a magnitude and a direction, measuring angles from the positive x$ direction.

Accepted Answer

$$10\ 	ext{m/s}^2$$, $$323^{\circ}$

Question 6

A projectile is fired from a cliff with initial velocity components $$v_{0x} = 60.0\ 	ext{m/s}$$ and $$v_{0y} = 80.0\ 	ext{m/s}. $$What is the vertical velocity component after $$21.0\ 	ext{s}$$?

Accepted Answer

$$v_y = 80.0 - 9.8 	imes 21.0$$

Question 7

A package dropped from an airplane at altitude $$h$$ and speed $$v$$ will hit the ground at an angle $$	heta$$ below the horizontal. If the package lands at $$32.1^{\circ}$$ below the horizontal, which of the following best describes the velocity components just before impact?

Accepted Answer

The horizontal component is unchanged, and the vertical component increases due to gravity.

Question 8

A child throws a ball with an initial speed of $$6.00\ 	ext{m/s} at$$ $$40.0^{\circ}$$ above the horizontal from a height of $$1.00\ 	ext{m}. $$How long is the ball in flight before it hits the ground?

Accepted Answer

$$1.22\ 	ext{s}$$

Question 9

A projectile is launched from a cliff with initial velocity $$v_0 at $$angle $$	heta$$ above the horizontal. If the projectile lands at distance $$D$$ from the base of the cliff, which equation best describes the horizontal displacement?

Accepted Answer

$$D = v_0$ \cos	heta \cdot t$$

Question 10

A hobby rocket lands $$2.00\ 	ext{km}$$ from the launch point after reaching a height of $$1.00\ 	ext{km}. $$Which formula would you use to determine the launch angle?

Accepted Answer

$$	an	heta = \frac{h}{D}$$

Question 11

A projectile is fired from a cliff with initial velocity $$v_0 at $$angle $$	heta. If $$the time of flight is $$T$$, what is the vertical displacement at time $$t$$?

Accepted Answer

$$y = v_0$ \sin	heta \cdot t - \frac{1}{2} g t^2$

Question 12

A Frisbee's velocity at time $$t is $$given by $$\vec{v}(t) = \frac{dx}{dt} \hat{i} + \frac{dy}{dt} \hat{j}. If$$ $$x(t) = 3t$$ and $$y(t) = 4t - 5t^2$, what is the magnitude of the velocity at t = 0.2$$\ 	ext{s}$$?

Accepted Answer

$$4\ 	ext{m/s}$$

Question 13

An airplane drops a package from altitude $$h$$ with horizontal speed $$v. $$Ignoring air resistance, what is the time it takes for the package to reach the ground?

Accepted Answer

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

Question 14

A projectile is launched horizontally from a cliff. Which statement best describes its motion?

Accepted Answer

The horizontal velocity remains constant, while the vertical velocity increases linearly with time due to gravity.

Question 15

A child throws a ball at $$40.0^{\circ}$$ above the horizontal. Which equation gives the initial vertical velocity component?

Accepted Answer

$$v_{0y} = v_0$ \sin 40.0$$^{\circ}$$

Question 16

A projectile is launched from a cliff with initial velocity $$v_0 at $$angle $$	heta. If $$the projectile lands at distance $$D$$ from the base, which equation best describes the time of flight?

Accepted Answer

$$t = \frac{D}{v_0$ \cos	heta}$$

Question 17

A projectile is fired from a cliff with initial velocity $$v_0 at $$angle $$	heta. If $$the projectile lands at distance $$D$$ from the base, which equation best describes the maximum height reached?

Accepted Answer

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

Projectile Motion: Velocity After a Given Time

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