An object is projected in the air with initial velocity u at an angle θ. The projectile motion is such that the horizontal range R, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be degree.

Question

An object is projected in the air with initial velocity u at an angle θ. The projectile motion is such that the horizontal range R, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be degree. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

R max =( u 2 sin 2(45°)/ g )=( u 2/ g ) ( R /2)=( u 2/2 g )=( u 2 sin 2 θ/ g ) sin 2 θ=(1/2) 2 θ=30°, 150° θ=15°, 75°

Rmax​=gu2sin2(45∘)​=gu2​ 2R​=2gu2​=gu2sin2θ​ sin2θ=21​ 2θ=30∘,150∘ θ=15∘,75∘

$R_{m a x} = \frac{u ^{2} s i n 2 ( 4 5 ^{\circ} )}{g} = \frac{u ^{2}}{g}$
$\frac{R}{2} = \frac{u ^{2}}{2 g} = \frac{u ^{2} s i n 2 θ}{g}$
$sin 2 θ = \frac{1}{2}$
$2 θ = 3 0^{\circ}, 15 0^{\circ}$
$θ = 1 5^{\circ}, 7 5^{\circ}$