A ball with mass \( m \) projected horizontally off the end of a table with an initial kinetic energy \( K \). At a time \( t \) after it leaves the end of the table it has kinetic energy \( 3 K \). What is \( t \) ? Neglect air resistance. (A) \( (3 / g ) \sqrt{ K / m } \) (B) \( (2 / g ) \sqrt{ K / m } \) (C) \( (1 / g ) \sqrt{8 K / m } \) (D) \( ( K / g ) \sqrt{6 / m } \)

Question

Please log in or register to answer this question.

Eshwarojha · Answer 1 · 2023-11-27T04:42:26+0000

(B) \(\frac{2}{g}\sqrt{\frac{K}{m}}\)

A ball with mass m is projected horizontally with an initial kinetic energy k and becomes 3k in time, t.

By work-Energy theorem

\(W_{net}=\triangle K.E.\)

⇒ \(W_{gravity}=3K-K\)

⇒ mgh = 2K

where, h is the height fallen in time t.