Assertion The range of a projectile is maximum at 45°. Reason At θ=45°, the value of sin θ is maximum.

Question

Assertion The range of a projectile is maximum at 45°. Reason At θ=45°, the value of sin θ is maximum. (A) Both Assertion and Reason are correct and Reason is the correct explanation of Assertion. (B) Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion. (C) Assertion is correct but Reason is incorrect. (D) Assertion is incorrect but Reason is correct.

Tardigrade Admin · Accepted Answer

Horizontal range, R=(u2 sin 2 θ/g) At, θ=45°, sin 2 θ=1 ∴ R max =(u2/g)= maximum range ∵ sin θ=1 (maximum), at θ=90° Therefore, Assertion is correct but Reason is incorrect.

Q. Assertion The range of a projectile is maximum at $4 5^{\circ}$ .
Reason At $θ = 4 5^{\circ}$ , the value of $sin θ$ is maximum.

Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

Assertion is correct but Reason is incorrect.

Assertion is incorrect but Reason is correct.

Horizontal range, $R = \frac{u ^{2} s i n 2 θ}{g}$
At, $θ = 4 5^{\circ}, sin 2 θ = 1$
$∴ R_{m a x} = \frac{u ^{2}}{g} =$ maximum range
$∵ sin θ = 1$ (maximum), at $θ = 9 0^{\circ}$
Therefore, Assertion is correct but Reason is incorrect.

Q. Assertion The range of a projectile is maximum at 45∘. Reason At θ=45∘, the value of sinθ is maximum.