Question

Mr. Letourneau is flying his broom stick parallel to the ground. He undergoes two consecutive displacements. The first is 100 km 10 degrees west of north, and the second is 120 km 50 degrees east of north. What is the magnitude of the broom stick's displacement?

Answer 1

Answer:190.78 km

Step-by-step explanation:

Given

First Displacement is
`100 km ^(\circ)`west of north

Position Vector
`(r_1)`of displacement is given by

`\vec{r_1}=100cos10\hat{j}-100sin10\hat{i}`

`\vec{r_1}=98.48\hat{j}-17.36\hat{i}`

Considering East as X axis and North Y axis

second displacement is 120 km
`50^(\circ)` east of north

Now position Vector of second Position w.r.t to first

`\vec{r_(21)}=120cos50\hat{j}+120sin50\hat{i}`

`\vec{r_(21)}=77.13\hat{j}+91.92\hat{i}`

`\vec{r_2}=\vec{r_1}+\vec{r_(21)}`

`\vec{r_2}=98.48\hat{j}-17.36\hat{i}+77.13\hat{j}+91.92\hat{i}`

`\vec{r_2}=74.56\hat{i}+175.61\hat{j}`

magnitude of displacement

`|r_2|`=190.78 km