boy moves with a velocity of 0.5ˆi−ˆj0.5𝑖^-𝑗^ ms–1. He finds rain at a velocity of 0.5ˆi−2ˆj0.5𝑖^-2𝑗^ ms–1. The speed of rain drop is
Question
The boy moves with a velocity of
ms<sup>–1</sup>.
He finds rain at a velocity of
ms<sup>–1</sup>.
The speed of rain drop is?
Solution
The velocity of the rain as observed by the boy is given by the vector difference of the velocity of the rain and the velocity of the boy.
The velocity of the rain as observed by the boy = velocity of the rain - velocity of the boy
= (0.5i - 2j) - (0.5i - j) = 0.5i - 2j - 0.5i + j = -j m/s
The speed of the rain drop is the magnitude of the velocity vector. In this case, the velocity of the rain drop is -j m/s, which is in the negative y-direction.
The magnitude of this vector is 1 m/s.
So, the speed of the rain drop is 1 m/s.
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