A ball is thrown vertically up ward. It has a speed of 10m/sec when it has reached one half of its m

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2.Motion in Straight Line

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A ball is thrown vertically up ward. It has a speed of $10\;m/sec$ when it has reached one half of its maximum height. How high ($m$ માં) does the ball rise? (Take $g = 10 \;m/s^2$)

A

$5$

B

$10$

C

$15$

D

$20$

(AIPMT-2001) (AIPMT-2005)

Solution

(b) Let particle thrown with velocity $u$ and its maximum height is $H$ then $H = \frac{{{u^2}}}{{2g}}$

When particle is at a height $H/2$, then its speed is $10\, m/s$

From equation ${v^2} = {u^2} – 2gh$

${(10)^2} = {u^2} – 2g\left( {\frac{H}{2}} \right) = {u^2} – 2g\frac{{{u^2}}}{{4g}}$$ \Rightarrow {u^2} = 200$

Maximum height $ \Rightarrow H = \frac{{{u^2}}}{{2g}} = \frac{{200}}{{2 \times 10}} = 10\;m$

Standard 11

Physics

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