Question

A car travels 10 km southeast and

Answer 1

$\bold{\huge{\green{\underline{Solution}}}}$

• A car travels 10 km southeast and then 15 km in a direction 60° north of east

$\bold{\underline{ To\: Find }}$

• We have to find the magnitude of the car of resultant vector

$\bold{\underline{ Let's \: Begin }}$

Here,

• In South east, car travels = 10km

• In North of east, it travels = 15km

• Angle between south east and north east is 60°

Therefore,

According to parallelogram law of resultant vector

If two vectors are represented by two adjacent sides of a parallelogram drawn from a point , the their resultant is equal to the diagonal of the parallelogram.

That is,

$\sf{ R = AC² = A² + B²}$

But, we have to calculate the magnitude of the resultant vector

$\sf{ | R |= √A² + B² + 2ABCosΦ }$

Subsitute the required values,

$\sf{ | R |=√ (10)² + (15)² + 2× 10 × 15 × cos 60° }$

$\sf{ | R | =√ 100 + 225 + 20 × 15 × 1/2}$

$\sf{ | R | = √100 + 225 + 10 × 15 }$

$\sf{ | R | = √335 + 150 }$

$\sf{ | R | = √485 }$

$\sf{\red{ | R | = 22.02 \: km}}$

Hence, The magnitude of the car resultant vector is 22.02 km.