Physics, asked by kamal8744, 11 months ago

A ball rolls off the top of a staircase with a horizontal velocity u m//s. If the steps are h meter high and b meter wide, the ball will hit the edge of the nth steps, if:

Answers

Answered by Anonymous
34

Solution

Given

  • The height of each step is h m
  • The breadth of each step is b m
  • Initial Velocity is u (along horizontal)

Here,the ball hits the edge of the nth step :

  • The distance covered along vertical would be 'nh' m
  • The breadth covered would be 'nb'm

To finD

Value of n

From,

 \sf \:  speed =  \dfrac{distance}{time}  \\  \\  \longrightarrow \:  \sf \: u =  \dfrac{nb}{t}  \\  \\  \longrightarrow \:  \sf \: nb = ut  \\  \\  \longrightarrow \:  \sf \: t =  \dfrac{nb}{u}  -  -  -  -  -  -  -  - (1)

Along the Height,

  • Initial Velocity is zero

 \sf \: nh = 0 +  \dfrac{1}{2} g {t}^{2}  \\  \\  \dashrightarrow \:  \sf \: nh =  \dfrac{1}{2}  \times g \times ( \dfrac{nb}{u} ) {}^{2}  \\  \\  \dashrightarrow \:  \sf \: nh =  \dfrac{ {n}^{2} {b}^{2}  }{2 {u}^{2} }  \times g \\  \\  \dashrightarrow \:  \boxed{ \boxed{ \sf{n = 2 \dfrac{h {u}^{2} }{g {b}^{2} } }}}

Similar questions