Scoring: | ||

Part I. | 1. | |

2. | ||

3. | ||

4. | ||

5. | ||

6. | ||

7. | ||

8. | ||

Part II. | 1. | |

2. | ||

Total: |

Practice

Closed book.

Use g = 10 m/sec2

1. The units of acceleration are:

- m/s
- m/s
^{2} - m
^{2}/s - m
^{2}/s^{2}

2. The equation v = v_{o} + at^{2} describes
the velocity of a particle, and a is its acceleration on the way. Which term
below is dimensionally correct?

- v
_{o} - at
^{2} - both terms
- neither term

What is the correct dimension of the entire equation?

- m/s
- m/s
^{2} - m
^{2}/s - m
^{2}/s^{2}

3. At a construction site a pipe wrench struck the ground with a speed of 20 m/s.

- How long was it falling?
- From what height was it inadvertently dropped?

4. If the vector **a** = 2**i** + 3 **j**,
what is the magnitude of **a**?

- 5
- 13
- 10

Draw approximately, where the vector is pointing

5. The angle between the
vector **a** in question 4.) and the positive x axis is:

- tan
^{-1}2/3 - tan
^{-1}3/2 - cos
^{-1} - sin
^{-1}

6. If ** **what is the magnitude of ?

- 3
- 4
- 5

In which quadrant of the coordinate system is the vector?

- 1st Quadrant
- 2nd
- 3rd
- 4th

7. What is the magnitude of the centripetal acceleration of a sprinter running
at 10 m/s when

rounding a turn with a radius of 25 m?

8. At a certain instant, a fly ball has velocity .The x axis is horizontal, the y axis is upward, and is in meters per second.

- The ball has not reached its highest point on its trajectory.
- The ball is at its highest point.
- The ball has passed its highest point on its trajectory.
- The equation gives us no information where the ball might be.

II.1. A small ball rolls horizontally off the edge of a tabletop that is 1.25 m high. It strikes the floor at a point 1.5 m horizontally away (in the positive x direction) from the edge of the table. (30 points)

- How long is the ball in the air?
- What is its speed at the instant it leaves the table?
- What is the vector velocity (give x and y component, including signs) of the ball when it hits the ground?

II.2. A kid throws a stone from the edge of the building with height h = 15
m, as shown below. The initial velocity of the stone is v_{ox} = 20
m/s and v_{oy} = 10 m/s.

- At which time after the stone is thrown does it reach its maximum height?
- What is the maximum height H above ground reached by the stone?
- Give the final velocity in vector notation of the stone when it hits the ground. Start with the component notation (mind the signs!), and then provide also magnitude and angle (relative to the positive x-axis) of the vector.