Question

eselasie3. A particle is displaced from the point (-4 m, -8 m) to the point (9 m, -1 m) in 30 seconds.Calculate the magnitude of its average velocity. (1 point)0.409 mA.B. O 0.492 mC. O 0.752 mD. 0.332 mE. O 0.565 m4. A bullet is fired horizontally from a 70 mtall building with a speed of 1400 m/s.How long will it take to hit the ground? (1 point)A. 03.78 SB6,558 s

Answer 1

The average velocity of a particle is given by:

`\vec{v}=\frac{\Delta\vec{r}}{t}`

To find the change in position we subtract the initial point to the final point, then we have:

`\begin{gathered} \Delta\vec{r}=\langle9-(-4),-1-(-8)\rangle \\ \Delta\vec{r}=\langle13,7\rangle \end{gathered}`

Now that we have the change in position we divide it by the time, then:

`\vec{v}=\frac{\Delta\vec{r}}{t}=(1)/(30)\langle13,7\rangle=\langle(13)/(30),(7)/(30)\rangle`

Hence, the average velocity is:

`\vec{v}=\langle(13)/(30),(7)/(30)\rangle`

To find is magnitude we need to remember that the magnitude of any vector is given by:

`v=√(v_x^2+v_y^2)`

Then, in this case, we have:

`\begin{gathered} v=\sqrt{((13)/(30))^2+((7)/(30))^2} \\ v=0.492 \end{gathered}`

Therefore, the magnitude of the average velocity is 0.492 m/s