Question

A ball is rolls the top of stairs way with a horizontal velocity of magnitude 2m/s.the steps are 10cm high and 20 cm wide.if g=10m/s^2.then the baball hits first the edge of ....
A) 1st. B) 2nd. C) 3rd. E) 4th

Answer 1

Answer on Question #48668, Physics, Mechanics | Kinematics | Dynamics

A ball is rolls the top of stairs way with a horizontal velocity of magnitude $2\mathrm{m/s}$. The steps are 10cm high and 20 cm wide. If $g=10\mathrm{m/s}^2$, then the ball hits first the edge of ...

A) 1st. B) 2nd. C) 3rd. E) 4th

Solution:

If the ball hits $n$th step, the horizontal and vertical distances traversed are $nw$ and $nh$ respectively.

$$w = 20 \text{ cm},$$ $$h = 10 \text{ cm}.$$

Let $t$ be the time taken by the ball for this horizontal and vertical displacement.

$$x = nw = vt$$ $$y = nh = \frac{gt^2}{2}$$

From first equation

$$t = \frac{nw}{v}$$

From second equation

$$nh = \frac{g}{2} \left(\frac{nw}{v}\right)^2$$

The number of steps is

$$n = \frac{2hv^2}{gw^2} = \frac{2 \times 0.1 \times 2^2}{10 \times 0.2^2} = 2$$

Answer: B) 2nd.

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