Question

Car X is travelling at 30m/s north. Its driver looks at car Y approaching on another road and he estimates it is moving at 15m/s south-west relative to his car. Calculate the velocity of car Y relative to the ground.

Answer 1

Answer: 22.1 m/s

Step-by-step explanation:

The velocity of Car traveling 30 m/s towards the north

In vector form it is

`v_x=30\hat{j}`

The velocity of car Y w.r.t X is

`\Rightarrow v_(yx)=15[-\cos 45^(\circ)\hat{i}-\sin 45^(\circ)\hat{j}]`

Solving this

`\Rightarrow v_(yx)=v_y-v_x\\\Rightarrow v_y=v_(yx)+v_x`

putting values

`\Rightarrow v_y=15[-\cos 45^(\circ)\hat{i}-\sin 45^(\circ)\hat{j}]+30\hat{j}`

`\Rightarrow v_y=-10.606\hat{i}+19.39\hat{j}`

absolute velocity relative to ground is

`\left | v_y\right |=√((-10.606)^2+(19.39)^2)\\\left | v_y\right |=22.101\ m/s`