Question

A hiker begins a trip by first walking 23.5 km

southeast from her base camp. On the second

day, she walks 40.5 km in a direction 69.3

◦

north of east, at which point she discovers a

forest ranger’s tower.

Determine the y component of the total

displacement.

Answer in units of km.

002 (part 2 of 3) 10.0 points

Find the magnitude of the resultant displace-

ment.

Answer in units of km.

003 (part 3 of 3) 10.0 points

Find the angle θ that the vector R = A + B

makes with the positive x axis, use counter-

clockwise as the positive angular direction,

between the limits of −180◦

and +180◦

Answer 1

$AB=23.5~km,~BC=40.5~km,$

1)

$AC_y=BC_y-AB_y=BC\sin 69.3°-AB\sin 45°=21.3~km,$

2)

$AC_x=AB_x+BC_x=AB\cos 45°+BC\cos 69.3°=30.9~km,$

$AC=\sqrt{AC_x^2+AC_y^2}=37.5~km,$

3)

$\theta=\arctan\frac{AC_y}{AC_x}=34.6°.$