Question

A car is driven east for a distance of 47 km, then north for 23 km, and then in a direction 32° east of north for 27 km. Determine (a) the magnitude of the car's total displacement from its starting point and (b) the angle (from east) of the car's total displacement measured from its starting direction.

Answer 1

(a). The car's total displacement from its starting point is 76.58 m.

(b). The angle of the car's total displacement measured from its starting direction is 36.81°.

Step-by-step explanation:

Given that,

Distance = 47 km in east

Distance = 23 km in north

Angle = 32° east of north

Distance = 27 km

According to figure,

Angle = 90-32 = 58°

(a). We need to calculate the magnitude of the car's total displacement from its starting point

Using Pythagorean theorem

`AC=√(AB^2+BC^2)`

`AC=√((47+27\cos58)^2+(23+27\sin58)^2)`

`AC=76.58\ m`

The magnitude of the car's total displacement from its starting point is 76.58 m.

(b). We need to calculate the angle (from east) of the car's total displacement measured from its starting direction

Using formula of angle

`\tan\theta=(y)/(x)`

put the value into the formula

`\theta=tan^(-1)(23+27\sin58)/(47+27\cos58)`

`\theta=tan^(-1)0.7486`

`\theta=36.81^(\circ)`

Hence, (a). The car's total displacement from its starting point is 76.58 m.

(b). The angle of the car's total displacement measured from its starting direction is 36.81°.