Q: Joe tracks Fido's movement: (1) Fido moves 100 m at $$32^ ext{o}$$ North of East, (2) then 200 m due South. What is Fido's total displacement from the starting point?

$$ ext{Displacement} \\approx 223 m at$$ $$74^ ext{o}$$ South of East

Q: A projectile is launched at an angle $$ heta$$ with initial speed $$v_0. $$Which of the following expressions gives the maximum height reached by the projectile?

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

Question 1

A dog named Fido moves along a straight line, and his position as a function of time is given by $$x(t) = 2t^2$ - 6t + 4 ($$where $$x is in $$meters and $$t in $$seconds). What is Fido's velocity at $$t = 5.5 s$$?

Accepted Answer

$$v = 10 m/s$$

Question 2

Given the position function $$x(t) = 2t^2$ - 6t + 4$$, is Fido's acceleration constant or changing? Justify your answer.

Accepted Answer

Constant, because the second derivative of $$x(t) is a $$constant.

Question 3

At what time(s) does Fido have zero velocity, given $$x(t) = 2t^2$ - 6t + 4$$?

Accepted Answer

$$t = 1.5 s $$and $$t = 2 s$$

Question 4

A vector $$	extbf{A}$$ has components $$A_x = 210 m $$and $$A_y = 227 m. $$What is the magnitude of $$	extbf{A}$$?

Accepted Answer

$$|	extbf{A}| = 317 m$$

Question 5

Joe tracks Fido's movement: (1) Fido moves 100 m at $$32^	ext{o}$$ North of East, (2) then 200 m due South. What is Fido's total displacement from the starting point?

Accepted Answer

$$	ext{Displacement} \approx 223 m at$$ $$74^	ext{o}$$ South of East

Question 6

If it takes 8.0 minutes for Fido to travel from point H to C, and the displacement is $$223 m$$, what is Fido's average velocity in SI unit vector notation?

Accepted Answer

$$	extbf{v}_{avg} = 0.47 m/s in $$the direction of displacement

Question 7

A small stone is dropped from rest from a height of $$100 m $$above the ground. Neglecting air resistance, what is the velocity of the stone $$2$$ seconds after it is dropped?

Accepted Answer

$$v = 19.6 m/s $$downward

Question 8

A ball is thrown toward a wall, $$27 m $$away, with an initial velocity $$v = 25 m/s at an $$angle of $$67^	ext{o}$$ above horizontal. How far above the release point does the ball strike the wall?

Accepted Answer

$$y = 24.8 m$$

Question 9

What are the horizontal and vertical components of the velocity when the ball strikes the wall, given $$v = 25 m/s at$$ $$67^	ext{o}$$?

Accepted Answer

$$v_x = 9.8 m/s$$, $$v_y = 8.7 m/s$$

Question 10

When the ball strikes the wall, has it passed the highest point of its trajectory?

Accepted Answer

Yes, because the vertical velocity is negative.

Question 11

A ball is thrown at $$t = 0$$ and follows a parabolic path. Which graph best represents the horizontal component of the velocity of the ball as a function of time?

Accepted Answer

A constant, nonzero value

Question 12

Which graph best represents the vertical component of the velocity of the ball as a function of time?

Accepted Answer

A linearly decreasing function

Question 13

A soccer player kicks a soccer ball as shown in the figure. Neglect air resistance. Does the ball spend more time in the air at point A, B, or C?

Accepted Answer

Same for both

Question 14

A high-speed train traveling at $$44.7 m/s $$comes upon a car moving at $$8.0 m/s in $$the same direction. If the train applies the brakes to reduce its speed to $$8.0 m/s$$, and the passenger then collides with the train's interior, what is the passenger's velocity relative to the train just before the collision?

Accepted Answer

$$v_{rel} = 36.7 m/s$$

Question 15

Which of the following best describes the acceleration of an object in free fall near Earth's surface (neglecting air resistance)?

Accepted Answer

It is constant and directed downward.

Question 16

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$Which of the following expressions gives the maximum height reached by the projectile?

Accepted Answer

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

Question 17

A car moves along a straight road with position given by $$x(t) = 4t^3$ - 2t^2$ + t. $$What is the car's acceleration at $$t = 2 s$$?

Accepted Answer

$$a = 36 m/s$^2$$

Question 18

A stone is thrown horizontally from a cliff $$80 m $$above the ground with a speed of $$10 m/s. $$How long does it take to hit the ground?

Accepted Answer

$$t = 4.0 s$$

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