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From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle to hit the ground is n time that taken by it to reach the highest to its path. Show that 2gH =nu²(n-2)

Jessy , 7 Years ago
Grade 11
anser 3 Answers
Soumya Ranjan Mohanty

Last Activity: 7 Years ago

Dear student,We know time to reach maximum height t1=u/g. t2 is time to reach ground is given by equation:-h=ut2 - 1/2 * g*t^2Given that t2=nt1 , putting value of t2 in above equation, we get 2gh=nu^2(n-2).Thanking you, Soumya Ranjan Mohanty.

tushar jaryal

Last Activity: 7 Years ago

As H is the height of tower
time taken by particle to reach highest point of its path is t=u/g
so speed on reaching ground,v=2+2gH>^2
now v=u + at
=>v= -u + gt’
=>2+2gH>^2= -u + gt[from above]
on solving
t’=[u+2+2gH>^2]/g 
given that time taken by particle to hit ground is n times that taken by it to reach the highest point.
=>t’=[u+2+2gH>^2]/g =nu/g
on solving
2gH=n[n-2]u2

Rishi Sharma

Last Activity: 4 Years ago

Dear Student,
Please find below the attached image of the solution to your problem.

Thanks and Regards
645-659_5.PNG

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