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At t=0, an arrow is fired vertically upw...

At `t=0`, an arrow is fired vertically upwards with a speed of `100 m s^(-1)`. A second arrow is fired vertically upwads with the same speed at `t=5 s`. Then .

A

The two arrows will be at the same height above the `t=20 s`,

B

The two arrows will reach back their starting points at `t=20 s` and at `t=25 s`.

C

The ratio of the speeds of the first and second arrow at`t= 20 s` will be `2 :1`.

D

The maximum height attained by either arrow will be `1000 m`,

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Let they meet at height `h` after time `t`.
`h=100 t-(1)/(2)g t^(2) rarr` for first aarow
`=100 (t-5) -(1)/(2) g (t-5)^(2) rarr` for decond arrow
`rArr t =- 12.5 s` (after solving ). So (a) is correct.
Time of flight of first arrow: `T=(2u)/(g) =(2xx 100)/(10) =20 s`
Second arrow will reach after `5 s` of reaching first. So `b` is rossect.
`{:(v_(1) =100 -10 xx 20 =- 100 m s^(-1))`,`(v_(2) =100 -10 xx 15 =-50 m s^(-1)):}`
Ratio: `(v_(1))/(v_(2))=2: 1. `So (c) is correct.
Maximum deight attained
`H=(u^(2))/(2g)=((100)^(2))/(2xx10)=500 m`. Hence, `d` incorrect.
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