JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Kinematics

Two bodies are projected from ground with same speeds

40 ms^{- 1}

at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of

6 0^{\circ}

, with horizontal then sum of the maximum heights, attained by the two projectiles, is ____ m. (Given

g = 10 ms^{- 2}

)

Answer: 80

Solution

Two launches at the same speed give equal ranges when their angles are complementary, so alongside the

6 0^{\circ}

throw there is one at

3 0^{\circ}

. The greatest height reached is

H = \frac{u ^{2} sin ^{2} θ}{2 g}

. For

6 0^{\circ}

H = \frac{4 0 ^{2} sin ^{2} 6 0 ^{\circ}}{2 \times 10} = \frac{1600 \times \frac{3}{4}}{20} = 60 m

; for

3 0^{\circ}

H = \frac{1600 \times \frac{1}{4}}{20} = 20 m

. Added together the two peak heights come to

80 m

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Integer answer