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
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
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.
Similar Questions
A raindrop was 18meters above the ground, falling straight down at a constant velocity. It took the raindrop 3seconds to fall half the distance to the ground. What was the raindrop's velocity?
A man holds an umbrella at 30∘ with the vertical to keep himself dry. He, then, runs at a speed of 10 ms−1 and finds the rain drops to be hitting vertically. Speed of the rain drops w.r.t the running man and w.r.t earth are
A rainstorm produces raindrops each with a mass of 7.5 × 10-5 kg and a terminal speed of 25 m/s. Suppose the rain is falling straight down (no wind).(a) [1 mark]What is meant by "terminal speed" and why does it exist?(b) [1 mark]While falling at terminal speed each rain drop is losing gravitational potential energy without gaining kinetic energy. Explain this in the context of conservation of energy.(c) [1 mark]Calculate the magnitude of the momentum of each rain drop. Suppose 560 drops of rain strike each square metre of ground every second. Consider a person stuck out in the rain. The top of their head has a cross-sectional area of 350 cm2.(d) [3 marks]Calculate the force of the rain hitting the person's head, assuming each rain drop comes to a stop?(e) [2 marks]Calculate the resulting pressure. Suppose a horizontal wind springs up giving the raindrops a horizontal velocity of 14 m/s, without changing their vertical velocity.(f) [2 marks]Calculate the momentum of a raindrop now, remembering that momentum is a vector quantity.
16. A boy spotted a bird on top of a VRA low tention wire. He shot an arrow straight up to hit the bird at an initial speed of 15.0 𝘮/𝘴. If the arrow misses the bird, after how much time is it moving downward at a speed of 8.00 𝘮/𝘴?
A raindrop of radius ‘r’ falls in air with terminal speed vt. What is the terminal speed of a raindrop of radius 2r
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.