Questions: Data Table 3: Changing the Drag Coefficient of a Projectile Drag Coefficient (m) Flight Time (s) Flight Range (m) Maximum Height (m) Initial Drag Force (N) --------------- 0.15 1.9 s 19.37 m 2.07 m 0.30 1.9 s 18.62 m 1.73 m 0.45 1.9 s 17.95 m 1.41 m 0.60 1.8 s 16.54 m 1.92 m 0.75 1.8 s 16.07 m 1.65 m

Data Table 3: Changing the Drag Coefficient of a Projectile

Drag Coefficient (m) Flight Time (s) Flight Range (m) Maximum Height (m) Initial Drag Force (N)
---------------
0.15 1.9 s 19.37 m 2.07 m
0.30 1.9 s 18.62 m 1.73 m
0.45 1.9 s 17.95 m 1.41 m
0.60 1.8 s 16.54 m 1.92 m
0.75 1.8 s 16.07 m 1.65 m

Transcript text: Data Experiment 2 5 Data Table 3 Photo 6 Photo 7 Exercise 2 Data Table 3: Changing the Drag Coefficient of a Projectile \begin{tabular}{ll|lll|} \begin{tabular}{l} Drag Coefficient \\ $(\mathrm{m})$ \end{tabular} & Flight Time $(\mathrm{s})$ & \begin{tabular}{l} Flight Range \\ $(\mathrm{m})$ \end{tabular} & \begin{tabular}{l} Maximum Height \\ $(\mathrm{m})$ \end{tabular} & \begin{tabular}{l} Initial Drag Force \\ $(\mathrm{N})$ \end{tabular} \\ 0.15 & 1.9 s & 19.37 m & 2.07 m & $\square$ \\ 0.30 & 1.9 s & 18.62 m & 1.73 m & \\ \hline 0.45 & 1.9 s & 17.95 m & 1.41 m & $\square$ \\ 0.60 & 1.8 s & 16.54 m & 1.92 m & $\square$ \\ 0.75 & 1.8 s & 16.07 m & 1.65 m & $\square$ \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Understanding the Problem

We are given a data table that shows the relationship between the drag coefficient of a projectile and various parameters such as flight time, flight range, maximum height, and initial drag force. Our task is to fill in the missing values for the initial drag force.

Step 2: Identifying the Formula for Drag Force

The drag force $ F_d $ can be calculated using the formula: \[ F_d = \frac{1}{2} \rho v^2 C_d A \] where:

$ \rho $ is the air density,
$ v $ is the velocity,
$ C_d $ is the drag coefficient,
$ A $ is the cross-sectional area.

Step 3: Analyzing the Given Data

We notice that the flight time is almost constant for different drag coefficients, which suggests that the initial velocity might be similar for these cases. However, without specific values for $ \rho $, $ v $, and $ A $, we cannot directly calculate the drag force. Instead, we can infer the relative changes in drag force based on the drag coefficient.

Step 4: Inferring the Initial Drag Force

Since the drag force is directly proportional to the drag coefficient $ C_d $, we can use the given drag coefficients to estimate the initial drag forces relative to each other.

Step 5: Calculating the Initial Drag Force

Assuming the initial drag force for $ C_d = 0.15 $ is $ F_{d0} $, we can express the other drag forces as multiples of $ F_{d0} $.

For $ C_d = 0.45 $: \[ F_d = 3 \times F_{d0} \]

For $ C_d = 0.60 $: \[ F_d = 4 \times F_{d0} \]

For $ C_d = 0.75 $: \[ F_d = 5 \times F_{d0} \]

Final Answer

\[ \boxed{ \begin{array}{ll|lll|} \begin{tabular}{l} Drag Coefficient \\ $(\mathrm{m})$ \end{tabular} & Flight Time $(\mathrm{s})$ & \begin{tabular}{l} Flight Range \\ $(\mathrm{m})$ \end{tabular} & \begin{tabular}{l} Maximum Height \\ $(\mathrm{m})$ \end{tabular} & \begin{tabular}{l} Initial Drag Force \\ $(\mathrm{N})$ \end{tabular} \\ 0.15 & 1.9 s & 19.37 m & 2.07 m & F_{d0} \\ 0.30 & 1.9 s & 18.62 m & 1.73 m & 2 \times F_{d0} \\ \hline 0.45 & 1.9 s & 17.95 m & 1.41 m & 3 \times F_{d0} \\ 0.60 & 1.8 s & 16.54 m & 1.92 m & 4 \times F_{d0} \\ 0.75 & 1.8 s & 16.07 m & 1.65 m & 5 \times F_{d0} \\ \hline \end{array} } \]

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