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

Answer:

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

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:

$D=\sqrt{(79km)^2+(65km)^2}=102km$

with an agle of:

$\alpha =arctg(\frac{79km}{65km})=51^o$