Question

plzz solve this with proper explanation​

Answer 1

Let the initial speed of both the projectile be u.

Now,

>>Given, the first projectile is thrown at an angle of (π/4+∅) = (45°+∅)

Range of projectile = usin2(45+∅)/g....(i)

>>The second projectile is thrown at an angle of (π/4-∅) = (45°-∅)

Range of projectile = usin2(45°-∅)/g...(ii)

Dividing eq(i) and (ii) we get,

Ratio of horizontal ranges described by the projectiles

=> usin2(45+∅)g-¹/usin2(45-∅)g-¹

=>sin2(45+∅)/sin2(45-∅)

=>sin(90+2∅)/sin(90-2∅)

{sin(90+∅) = cos∅ and sin(90-∅) = cos∅)

=>cos2∅/cos2∅

=>1:1

Therefore the correct option is (3) 1:1

Cheers!

Answer 2

Answer:

(4) 1 : 1

Explanation:

when the angle of projection of two projectiles having same speed are complementary to each other, their horizontal ranges are equal.

i.e.

if a and b are angle of projection and

a + b = π/2

Ranges of the two projectiles are equal.

here, a = π/4 - theta

and b = π/4 + theta

so, a + b = π/2

hence , R1 = R2

or, R1 : R2 :: 1 : 1