Request a call back

Join NOW to get access to exclusive study material for best results

Maharashtra Class 10 Answered

A stone thrown vertically upwards with initial velocity u reaches a height 'h' before coming down. Show that the time taken to go up is same as the time taken to come down.
Asked by akshaywbr | 17 Aug, 2018, 04:15: PM
answered-by-expert Expert Answer
we need to use the equations of motion, 
 
 v = u + a×t   .....................(1)
v2 = u2 + 2×a×S .................(2) 
 
where v is final velocity after time t, u is initial velocity, a is acceleration and S is distance travelled in time t.
 
 
Let u be the initial projection velocity of stone.
when the stone reaches the maximum height after time t , its final velocity is zero. 
When the stone travelling vertically upwards, it is experiencing the retardation due to gravity.
 
hence we write the above equation of motion (1) as, 0 = u - g×t or t = u/g .............(3)
 
eqn.(2) will be written as,   0 = u2 - 2×g×h,  or  begin mathsize 12px style u space equals space square root of 2 cross times g cross times h end root space end style...................(4)
 
by substituting u from eqn.(4) in eqn.(3), we have t begin mathsize 12px style equals space u over g space equals space fraction numerator square root of 2 cross times g cross times h end root over denominator g end fraction space equals space square root of fraction numerator 2 cross times h over denominator g end fraction end root end style............(5)
After reaching maximum height, the stone descends with zero initial velocity, 
accelerated downwards due to gravity and reaches the ground after time t'.
 
Eqns.(1) and (2) are written as follows for downward travel
 
v = 0+gt'  or  t' = v/g ..........................(6)
 
v2 = 0+2gh or begin mathsize 12px style v space equals space square root of 2 cross times g cross times h end root end style .....................(7)
 
from eqn.(4) and eqn.(7), we can conclude that initila projection velocity and
final velocity when the stone reaches the ground are equal
 
by substituting for v from eqn.(7) in eqn.(6), we get ,  begin mathsize 12px style t apostrophe space equals space v over g space equals space fraction numerator square root of 2 cross times g cross times h end root over denominator g end fraction space equals space square root of fraction numerator 2 cross times h over denominator g end fraction end root end style................(8)
from eqn.(5) and eqn.(8),  time of ascending the height h is equal to time of descending from same height h
Answered by Thiyagarajan K | 17 Aug, 2018, 08:58: PM
Maharashtra 10 - Physics
Asked by 16msas0711 | 29 May, 2023, 11:13: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Maharashtra 10 - Physics
Asked by vedantwaje8 | 29 Sep, 2022, 10:00: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Maharashtra 10 - Physics
Asked by hiyajain001 | 29 Dec, 2021, 09:40: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Maharashtra 10 - Physics
Asked by dilippaithane749 | 12 Feb, 2021, 09:50: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Maharashtra 10 - Physics
Asked by vedhikanaik2004 | 23 Dec, 2020, 09:07: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Maharashtra 10 - Physics
Asked by Tejalkothari3427 | 06 Sep, 2020, 09:38: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Maharashtra 10 - Physics
Asked by anuragtayde2004 | 08 Jul, 2020, 11:28: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Maharashtra 10 - Physics
Asked by nisharkinnary | 01 Jan, 2020, 03:40: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Maharashtra 10 - Physics
Asked by adityamhatre10518 | 22 Dec, 2019, 08:06: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Get Latest Study Material for Academic year 24-25 Click here
×