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Physics-

General

Easy

Question

A projectile is thrown in the upward direction making an angle of $60 degree$ with the horizontal direction with velocity of $147 blank m s to the power of negative 1 end exponent$ . Then the time after which its inclination with the horizontal is $45 degree$ , is

25 s
10.98 s
5.49 s
2.745 s

The correct answer is: 5.49 s

$H o r i z o n t a l blank c o m p o n e n t blank o f blank v e l o c i t y blank a t blank a n g l e blank 60 degree equals H o r i z o n t a l blank c o m p o n e n t blank o f blank v e l o c i t y blank a t blank a n g l e blank 45 degree$
$i e comma cos invisible function application 60 degree equals u cos invisible function application 45 degree$
$147 cross times fraction numerator 1 over denominator 2 end fraction equals v cross times fraction numerator 1 over denominator square root of 2 end fraction$
$o r blank v equals fraction numerator 147 over denominator square root of 2 end fraction m s to the power of negative 1 end exponent$
vertical component of velocity at angle $60 degree$
$u equals u sin invisible function application 60 degree equals fraction numerator 147 square root of 3 over denominator 2 end fraction m$
vertical component of velocity at angle $45 degree equals v sin invisible function application 45 degree$
$equals fraction numerator 147 over denominator square root of 2 end fraction cross times fraction numerator 1 over denominator square root of 2 end fraction equals fraction numerator 147 over denominator 2 end fraction m$
$B u t blank v subscript y end subscript equals u subscript y end subscript plus a t$
$therefore blank fraction numerator 147 over denominator 2 end fraction equals fraction numerator 147 square root of 3 over denominator 2 end fraction minus 9.8 t$
$o r blank 9.8 t equals fraction numerator 147 over denominator 2 end fraction open parentheses square root of 3 minus 1 close parentheses$
$therefore blank t equals 5.49 blank s$

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