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# If t1andt2 are the times of flight for two complimentary angles then the range of projectile R is.???

Ravneet
104 Points
2 years ago
complimentary angles :   two angles whose sum is 90°.
RANGE OF PROJECTILE   =      ( u2 sin2x)/g            where x = angle
so sin2x = 2sinxcosx if angles are complimentry ,say , a and 90-a
sin2a = 2sinacosa
sin2(90-a) = 2sin(90-a)cos(90-a) = 2cosasina
Now t1 and t2 be two time of flight
As sin2x is same , u and g are constant
so t1 = t2

Arun
25763 Points
2 years ago
Dear student

R = u² sin2A /g

Now

R = u² sin 2(90-A) /g

R = u² sin 2A/g

Same Range

Hence of a particle is projected woth two complimentary angles, its range is same
Ravneet
104 Points
2 years ago
it means the range is same for complementary angles
range for t1 = range for t2.
example :

For complementary angles, the two possible sets could be -

θ1 = 30 deg , θ2 = 60 deg; or

θ1 = 60 deg , θ2 = 30 deg

For all of the above angles of projection, sin 2θ comes out to be the same value