Question

At one instant a bicyclist is 25 m due east of a park's flagpole, going due south with a speed of 9 m/s. Then, 27 s later, the cyclist is 60 m due north of the flagpole, going due east with a speed of 13 m/s. For the cyclist in this 27 s interval, find each of the following. (a) displacement magnitude 1 m direction 2 ° north of west (b) average velocity magnitude 3 m/s direction 4 ° north of west (c) average acceleration magnitude 5 m/s2 direction 6 ° north of east.

Answer 1

Step-by-step explanation:

Given

`\vec{r_1}=25\hat{i}`

`\vec{v_1}=-9\hat{j} m/s`

after 27 s

`\vec{r_2}=60\hat{j}`

`\vec{v_2}=13\hat{i}`

Displacement
`=\vec{r_2}-\vec{r_1}`

`=60\hat{j}-25\hat{i}`

(b)
`v_(avg)=(Diplacement)/(time)`

`v_(avg)=\frac{60\hat{j}-25\hat{i}}{27}`

Magnitude of v_{avg}[/tex]

`|v_(avg)|=\sqrt{\left ( (25)/(27)\right )^2+\left ( (60)/(27)\right )^2}`

`|v_(avg)|=2.407 m/s`

direction

`tan\theta =(60)/(25)=2.4`

`\theta =67.38^(\circ)` North of west

(c)Average acceleration

`a_(avg)=(Change in velocity)/(time)`

`a_(avg)=\frac{13\hat{i}+9\hat{j}}{27}`

`a_(avg) is\ magnitude\ of\ |a_(avg)|`

`|a_(avg)|=\sqrt{\left ( (13)/(27)\right )^2+\left ( (9)/(27)\right )^2}`

`|a_(avg)|=0.58 m/s^2`