Certainly! Let's go through each part of the question step-by-step and complete the required calculations.
---
### Part (a)
Complete the following table:
[tex]\[
\begin{array}{|l|c|c|}
\hline
& \text{horizontal} & \text{vertical} \\
\hline
\text{initial velocity} & 217.51 \, \text{m/s} & 101.43 \, \text{m/s} \\
\hline
\text{acceleration} & 0 \, \text{m/s}^2 & -9.8 \, \text{m/s}^2 \\
\hline
\text{final velocity} & 217.51 \, \text{m/s} & -101.43 \, \text{m/s} \\
\hline
\end{array}
\][/tex]
#### Explanation:
- The initial horizontal velocity [tex]\(v_{0x}\)[/tex] is calculated using [tex]\( v_{0x} = 240 \cos(25^\circ) \)[/tex] which gives approximately [tex]\(217.51 \, \text{m/s}\)[/tex].
- The initial vertical velocity [tex]\(v_{0y}\)[/tex] is calculated using [tex]\( v_{0y} = 240 \sin(25^\circ) \)[/tex] which gives approximately [tex]\(101.43 \, \text{m/s}\)[/tex].
- The horizontal acceleration is [tex]\(0\, \text{m/s}^2\)[/tex] (since gravity only affects the vertical motion).
- The vertical acceleration is [tex]\( -9.8\, \text{m/s}^2\)[/tex] (due to gravity).
---
### Part (b)
How long is the bullet in the air?
The time of flight [tex]\( T \)[/tex] is given by:
[tex]\[
T = \frac{2 \cdot v_{0y}}{g} = \frac{2 \cdot 101.43}{9.8} \approx 20.70 \, \text{s}
\][/tex]
---
### Part (c)
What is the maximum height achieved by the bullet?
The maximum height [tex]\(H\)[/tex] is given by:
[tex]\[
H = \frac{{v_{0y}}^2}{2g} = \frac{(101.43)^2}{2 \cdot 9.8} \approx 524.88 \, \text{m}
\][/tex]
---
### Part (d)
How far away from the shooter does the bullet hit the ground?
The range [tex]\(R\)[/tex] is calculated using:
[tex]\[
R = v_{0x} \cdot T = 217.51 \cdot 20.70 \approx 4502.47 \, \text{m}
\][/tex]
---
To summarize:
- The initial horizontal velocity is [tex]\(217.51 \, \text{m/s}\)[/tex] and vertical velocity is [tex]\(101.43 \, \text{m/s}\)[/tex].
- The time of flight is approximately [tex]\(20.70 \, \text{s}\)[/tex].
- The maximum height achieved is approximately [tex]\(524.88 \, \text{m}\)[/tex].
- The range is approximately [tex]\(4502.47 \, \text{m}\)[/tex].
