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A body is fired with a velocity of magni...

A body is fired with a velocity of magnitude `sqrt(gR) lt V lt sqrt(2gR)` at an angle of `30^(@)` with the radius vector of earth. If at the highest point the speed of the body is `V//4`, the maximum height attained by the body is equal to:

A

`v^(2)//8g`

B

`R`

C

`sqrt(2)R`

D

None of the above

Text Solution

AI Generated Solution

To solve the problem step by step, we will use the concepts of angular momentum and the given conditions about the projectile motion of the body. ### Step 1: Understand the problem A body is fired with a velocity \( V \) such that \( \sqrt{gR} < V < \sqrt{2gR} \) at an angle of \( 30^\circ \) with the radius vector of the Earth. At the highest point, the speed of the body is \( \frac{V}{4} \). We need to find the maximum height \( h \) attained by the body. ### Step 2: Define angular momentum at the launch point The angular momentum \( L_A \) at the launch point can be expressed as: \[ ...
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