Question

7. Two projectiles A and B are thrown from the same
point with velocities v and v/2, respectively. If B is
thrown at an angle 45° with horizontal, what is the
inclination of A when their ranges are the same?​

Answer 1

Explanation:

given their ranges are same so applying Condition for range....

we let their i

v^2 sin2x/g = (v/2)^2 sin2×45° /g

v^2 sin 2x = v^2/4......( as g cancels and sin90° =1)

sin2x = 1/4

x = 1/2( sin inverse (1/4))

Answer 2

Given :-

Velocity of A = V

Velocity of B = V/2

${R}_{A} = {R}_{B}$

(V² Sin 2Ø)/g = [(V/2)² Sin 2Ø]/g

(V² Sin 2Ø) = V²/4 × Sin(2 × 45°)

Sin 2Ø = 1/4

2Ø = Sin-¹(1/4)

Ø = 1/2 [Sin-¹ (1/4)]

Ø = 1/2 Sin-¹ (1/8)

Hence,

The Inclination of A when their ranges are same = Ø = 1/2 Sin-¹(1/8).