Find solutions to your questions with the help of IDNLearn.com's expert community. Discover prompt and accurate answers from our experts, ensuring you get the information you need quickly.
Sagot :
In order to find the direction of the initial velocity, first let's calculate the change in velocity caused by the acceleration:
[tex]\begin{gathered} F=m\cdot a\\ \\ 2655=15.5\cdot a\\ \\ a=171.29\text{ m/s^^b2}\\ \\ \\ \\ \Delta V=a\cdot t\\ \\ \Delta V=171.29\cdot0.05\\ \\ \Delta V=8.5645\text{ m/s} \end{gathered}[/tex]Now, let's calculate the horizontal and vertical components of the final velocity.
The direction is N45W, therefore the angle is 90° + 45° = 135°:
[tex]\begin{gathered} V_x=V\cdot\cos135°=45\cdot(-\frac{\sqrt{2}}{2})=-31.82\text{ m/s}\\ \\ V_y=V\cdot\sin135°=45\cdot\frac{\sqrt{2}}{2}=31.82\text{ m/s} \end{gathered}[/tex]The change in the velocity occurred in north direction, so let's calculate the initial vertical velocity:
[tex]V_{iy}=V_y-\Delta V=31.82-8.5645=23.2555\text{ m/s}[/tex]Now, to calculate the direction, we can use the arc tangent below:
[tex]\theta=\tan^{-1}(\frac{V_{iy}}{V_{ix}})=\tan^{-1}(\frac{23.2555}{-31.82})=-36.16°[/tex]Since the direction is between north and west, we need to add 180° to the result, so the angle will be 143.84°.
This angle is equal to the direction N 53.84° W.
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. For trustworthy answers, rely on IDNLearn.com. Thanks for visiting, and we look forward to assisting you again.
