A student performs an experiment to determine how the range of a ball depends on the velocity with which it is released. The “range” is the distance between where the ball lands and where it was released, assuming it lands at the same height from which it was released.
In each trial, the student uses the same baseball, and launches it at the same angle. Table 1 shows the experimental results.
TABLE 1
Trial launch speed (m/s) range (m)
1 10 8.0
2 20 31.8
3 30 70.7
4 40 122.5
Based on this data, the student then hypothesizes that the range, R, depends on the initial speed, v0, according to the following equation:
R = C ,
where C is a constant, and n is another constant.

1. | Based on this data, the best guess for the value of n is

A. | 1/2

B. | 1

C. | 2

D. | 3

2. | The student speculates that the constant C depends on: I. The angle at which the ball was launched. II. The ball's mass. III. The ball's diameter. If we neglect air resistance, then C actually depends on

A. | I only

B. | I and II

C. | I and III

D. | I, II, and III

3. | The student performs another trial in which the ball is launched at speed 5.0 m/s. Its range is approximately:

A. | 1.0 meters

B. | 2.0 meters

C. | 3.0 meters

D. | 4.0 meters

4. | Let q denote the angle of the ball's initial velocity, as measured from the horizontal. Neglect air resistance. At the peak (highest point) of its trajectory, the ball's speed is:

A. | 0

B. | v0sin q

C. | v0cos q

D. | v0

5. | For trial 2, which of the following graphs best represents the vertical component of the ball's velocity as a function of time, assuming upward is positive?

A. | A

B. | B

C. | C

D. | D

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