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Galileo writes that for angles of projec...

Galileo writes that for angles of projection of a projectile at angles `(45 + theta)` and `(45 - theta)`, the horizontal ranges described by the projectile are in the ratio of (if `theta le 45`)

A

`2 : 1`

B

`1: 2`

C

`1 : 1`

D

`2 : 3`

Text Solution

Verified by Experts

The correct Answer is:
C
`R_(1) = (u^(2))/(g) sin{2(45 + theta)} = (u^(2))/(g) cos 2 theta`
`R_(2) = (u^(2))/(g) sin {2(45 - theta)} = (u^(2))/(g) cos 2 theta`
`(R_(1))/(R_(2)) = (1)/(1)`
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Knowledge Check

  • For angles of projection of a projectile at angle (45^(@) - theta) and (45^(@)+ theta) , the horizontal ranges described by the projectile are in the ratio of :

    A
    `1:1`
    B
    `2:3`
    C
    `1:2`
    D
    `2:1`

  • For angles of projection of a projectilc at angles (45 ^(@)-theta) "and" (45 ^(@)+ theta), the horizontal ranges described by the projectile are in the ratio of :

    A
    `1 :1 `
    B
    ` 2 : 3`
    C
    `1 : 2`
    D
    ` 3 : 2`

  • For angles of projection of a projectile at angles (45^(@) – θ) and (45^(@) + θ) , the horizontal ranges described by the projectile are in the ratio of:

    A
    ` 1 : 1 `
    B
    `2 : 3 `
    C
    ` 1 : 2 `
    D
    `2 : 1 `

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