Question for relative motion

Question

A car leaves point A and drives at 80.0 km/h [E] for 1.50 h. It then heads north at 60.0 km/h for 1.00 h and finally [30.0 W of N] at 100.0 km/h for 0.50 h, arriving at point B.

(a) Determine the displacement of point B from point A.

(b) A plane flies directly from point A to point B, leaving 2.00 h after the car has departed from point A. It arrives at point B at the same time the car arrives. There is a wind blowing at 60.0 km/h due south for the entire trip. What is the airplane’s airspeed?

Answer 1

Santusht, for this kind of relative motion problem, a diagram is essential.

Let's imagine the various points are on a norm X-Y grid. Call the 4 points A, C, D, B.

The coordinates are as follows:

A (0, 0)

C (120, 0) He drives east @ 80 km/h for 1.50 h => 120 km

D (120, 60) He drives north @ 60 km/h for 1 h => 60 km

B (120 - 50 cos 60^o, 60 + 50sin 60^o) Complete the right angled Δ with hypotenuse DB

= (120 - 25, 60 + 25√3) = (95, 60 + 25√3)

So the displacement of B from A is the distance BA = √(95² + (60 + 25√3)²)

= √(9025 + 3600 + (2 x 60 x 25√3) + (625 x 3))

= √(14,500 + 3000√3)

= 140.3 km