Question

Tammy leaves the office, drives 34 km due north, then turns onto a second highway and continues in a direction of 35◦ north of east for 79 km. What is her total displacement from the office? Answer in units of km. \ At what angle is her displacement? (C

Answer 1

The total displacement is 102 km
`51^o` north of east.

Step-by-step explanation:

We can treat this problem as a trigonometric one, so we need to calculate the total displacement on the north and east.

`d_n=34km+79km*sin(35^o)=79km`

and

`d_e=79*cos(35^o)=65km`

The total displacement is given by:

`D=√((79km)^2+(65km)^2)=102km`

with an agle of:

`\alpha =arctg((79km)/(65km))=51^o`