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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

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krlosdark12

Answer:

The total displacement is 102 km [tex]51^o[/tex] 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.

[tex]d_n=34km+79km*sin(35^o)=79km[/tex]

and

[tex]d_e=79*cos(35^o)=65km[/tex]

The total displacement is given by:

[tex]D=\sqrt{(79km)^2+(65km)^2}=102km[/tex]

with an agle of:

[tex]\alpha =arctg(\frac{79km}{65km})=51^o[/tex]

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