A projectile is projected at an angle > 45 degree with an initial velocity u. The time t, at which its horizontal velocity will be equal to vertical velocity is_________.

Asked by arijitodisha | 10th Jun, 2016, 09:12: PM

Expert Answer:

Question : A projectile is projected at an angle > 45 degree with an initial velocity u. The time t, at which its horizontal velocity will be equal to vertical velocity is_________.
 
begin mathsize 12px style The space angled space Projectile space Motion apostrophe straight s
Horizontal space velocity space component space is space given space by space colon negative
space space straight v subscript straight x space end subscript equals space straight u space cos open parentheses straight theta close parentheses
where space straight v subscript straight x space end subscript is space the space horizontal space velocity comma space straight u space is space the space initital space velocity space and space straight theta space is space the space angle space of space projectile

Vertical space velocity space component space is space given space by space colon negative
space straight v subscript straight y equals straight u space sin open parentheses straight theta close parentheses minus gt
where space space straight v subscript straight y space is space vertical space velocity comma straight u space is space the space initital space velocity comma space straight theta space is space the space angle space of space projectile comma space
straight g space is space the space acceleration space due space to space gravity space and space apostrophe straight t apostrophe space is space time space of space projectile.

The space time space apostrophe straight t apostrophe space at space which space the space horizontal space and space vertical space velocity space will space be space equal space is space given space by

space straight u space cos open parentheses straight theta close parentheses space equals space straight u space sin open parentheses straight theta close parentheses minus gt

gt equals straight u space sin open parentheses straight theta close parentheses minus space straight u space cos open parentheses straight theta close parentheses

gt equals straight u space left square bracket space sin open parentheses straight theta close parentheses minus space cos open parentheses straight theta close parentheses space right square bracket

straight t equals fraction numerator straight u space left square bracket space sin open parentheses straight theta close parentheses minus space cos open parentheses straight theta close parentheses space right square bracket over denominator straight g end fraction end style

Answered by Abhijeet Mishra | 27th Nov, 2017, 03:44: PM

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