Question

a body thrown vertically upwards with speed u reaches a maximum height h. if the speed is increased by three times then maximum height becomes xh. the value of x is.

Answer 1

A body thrown vertically upwards with speed u reaches a maximum height h. if the speed is increased by three times then maximum height becomes xh, the value of x is 9

Explanation:

Initial speed of the body = u

Final speed of the body v = 0

Height attained by the body = h

By the third equation of motion

$v^2=u^2-2gh$

$0^2=u^2-2gh$

$\implies h=\frac{u^2}{2g}$

Now if the speed is increased 3 times then

initial speed u = 3u

Therefore, height attained

$xh=\frac{(3u)^2}{2g}$

$\implies xh=9\frac{u^2}{2g}$

$\implies xh=9h$

$\implies x = 9$

Hope this answer is helpful.

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Answer 2

Given :

Speed of body = u

Maximum height when speed is u = h

New speed = 3u

New height when speed is 3u = xh

To find:

The value of x in xh .

Solution :

At maximum height , the final velocity , v = 0

Using 3rd law of motion ,

v^2 = u^2 - 2 * g * h

on putting the values ,

0 = u^2 - 2 * g * h

h = u^2 / ( 2*g )       .......(i)

when speed is 3u , the maximum height attained is xh .

using the equation  (n) , ans putting the values of h -> xh and u->3u ,

xh = (3u)^2 / ( 2*g )

xh = 9u^2 / ( 2*g )

xh = 9h          { using ( i ) }

x = 9

The value of x in xh is 9 .