Question

A car is driven east for a distance of 50 km, then north for 30 km, and then in a direction 30" east of north for 25 km. determine (a) the magnitude and (b) the angle of the car's total displacement from its starting point.​

Answer 1

pls refer the attachment first for better understanding

cos 60 = X/ 25

X = 25 cos 60

sin 60 =Y /25

Y= 25 sin 60

R x = 50 + 25 cos 60

R x = 50 +12.5

R x = 62.5 km

R y = 30 + 25 sin 60

R y 30 + 12.5√3

R y =21.6+30

R y=51.6 km

R =√ (51.6)²+(62.5)²

R= √2662.56 + 3906.25

R=√6568.81

R=81.04 km

$tan \alpha = \frac{ry}{rx}$

$tan \alpha = \frac{51 .6}{62.5}$

$\tan( \alpha ) = 0.82$

$\alpha = tan {(0.82)}^{ - 1}$

$\alpha = 39 °\: 21'$