Two projectiles are thrown with same initial velocity making an angle of 45° and 30° with the horizontal respectively. The ratio of their respective ranges will be

Question

Two projectiles are thrown with same initial velocity making an angle of 45° and 30° with the horizontal respectively. The ratio of their respective ranges will be (A) 1: √2 (B) √2: 1 (C) 2: √3 (D) √3: 2

Tardigrade Admin · Accepted Answer

Let projection speed is u R 1=( u 2 operatornameSin(90°)/ g ) ; R 2=( u 2 sin (60°)/ g ) ( R 1/ R 2)=(2/√3)

Q. Two projectiles are thrown with same initial velocity making an angle of $4 5^{\circ}$ and $3 0^{\circ}$ with the horizontal respectively. The ratio of their respective ranges will be

$1 : 2$

$2 : 1$

$2 : 3$

$3 : 2$

Let projection speed is $u$
$R_{1} = \frac{u ^{2} Sin ( 9 0 ^{\circ} )}{g}; R_{2} = \frac{u ^{2} s i n ( 6 0 ^{\circ} )}{g}$
$\frac{R _{1}}{R _{2}} = \frac{2}{3}$

Q. Two projectiles are thrown with same initial velocity making an angle of 45∘ and 30∘ with the horizontal respectively. The ratio of their respective ranges will be

1:2​

2​:1

2:3​

3​:2