A model rocket rests on a frictionless horizontal surface and is joined by a string of length `l` to a fixed point so that the rocket moves in a horizontal circular path of radius `l`. The string will break if its tensiion exceeds a value `T`. The rocket engine provides a thrust `F` of constant magnitude along the rocket's direction of motion. the rocket has a mass `m` that does not change with time. Answer the following questions based on the above passage.
What distance does the rocket travel between the time `t_(1)` when the string breaks and the time `2t_(1)`? The rocket engine continues of operate after the string breaks.

Options

A. `(3lT)/(2F)`
B. `(2lT)/(3F)`
C. `(lT)/(2F)`
D. `(2lT)/F`

Answer

A

Explanation

`S=v(2t_1-t_1)+1/2a_1(2t_1-t_1)^2`
`=F/mt_1(t_1)+1/2F/mt_1^2=3/2F/mt_1^2=3/2F/m(mlT)/F^2=(3lT)/(2F)`