Question

Ram was riding in a car travelling at a speed of $20m{s}^{-1}$ toward east. Shyam was standing on the sideway when the car passed him. Just before the car passed close to Shyam (when it was north-west of him); Ram had thrown a banana peel with velocity $10m{s}^{-1}$ relative to him as $v_{Banana,Ram}=(-10)\hat{i}+(-10)\hat{j}$. The banana peel had velocity components $10m{s}^{-1}$ toward south and $10m{s}^{-1}$ towards west in Ram's reference frame. When Ram met Shyam later, Shyam accused that Ram had thrown the banana peel at him. Explain this with the help of a velocity diagram.

Answer 1

The banana peel was thrown from a point in south-west direction relative to car (reference frame of Ram). Shyam is on the ground; the velocity of banana peel relative to him can be considered to be the absolute velocity of banana peel.
${\overrightarrow{v}}_{Banana/Ram}={\overrightarrow{v}}_{Banana}-{\overrightarrow{v}}_{Ram}$
$\Rightarrow {\overrightarrow{v}}_{Banana}={\overrightarrow{v}}_{Banana/Ram}+{\overrightarrow{v}}_{Ram}$
$=(-10)\hat{i}+(-10)\hat{j}+\left(20\right)\hat{i}=\left(10\right)\hat{i}-\left(10\right)\hat{j}$
i.e., the absolute velocity of banana peel is directed toward south-east, or toward Shyam as shown in Figure.