Three projectiles A, B and C are projected at an angle of 30° , 45° , 60° respectively. If RA, RB and RC are ranges of A, B and C respectively, then (velocity of projection is same for A, B and C)

Question

Three projectiles A, B and C are projected at an angle of 30° , 45° , 60° respectively. If RA, RB and RC are ranges of A, B and C respectively, then (velocity of projection is same for A, B and C) (A) RA = RB = RC (B) RA = RC > RB (C) RA < RB < RC  (D) RA = RC < RB

Tardigrade Admin · Accepted Answer

Range of projectile motion, R=(u2 sin (2 θ)/2 g) Longrightarrow R propto sin (2 θ) (∵ u is same for all ) Given: θ A =30° θ B =45° θ C =60° We know: sin (60°)=0.866 sin (90°)=1 sin (120°)=0.866 Longrightarrow R A = R C < R B

Q. Three projectiles $A, B$ and $C$ are projected at an angle of $3 0^{\circ}, 4 5^{\circ}, 6 0^{\circ}$ respectively. If $R_{A}, R_{B}$ and $R_{C}$ are ranges of $A, B$ and $C$ respectively, then (velocity of projection is same for $A, B$ and $C$ )

$R_{A} = R_{B} = R_{C}$

$R_{A} = R_{C} > R_{B}$

$R_{A} < R_{B} < R_{C}$

$R_{A} = R_{C} < R_{B}$

Q. Three projectiles A,B and C are projected at an angle of 30∘,45∘,60∘ respectively. If RA​,RB​ and RC​ are ranges of A,B and C respectively, then (velocity of projection is same for A,B and C)

RA​=RB​=RC​

RA​=RC​>RB​

RA​<RB​<RC​

RA​=RC​<RB​

Range of projectile motion, R=2gu2sin(2θ)​ ⟹R∝sin(2θ)(∵u is same for all ) Given : θA​=30∘θB​=45∘θC​=60∘ We know: sin(60∘)=0.866sin(90∘)=1sin(120∘)=0.866 ⟹RA​=RC​<RB​

Q. Three projectiles $A, B$ and $C$ are projected at an angle of $3 0^{\circ}, 4 5^{\circ}, 6 0^{\circ}$ respectively. If $R_{A}, R_{B}$ and $R_{C}$ are ranges of $A, B$ and $C$ respectively, then (velocity of projection is same for $A, B$ and $C$ )

$R_{A} = R_{B} = R_{C}$

$R_{A} = R_{C} > R_{B}$

$R_{A} < R_{B} < R_{C}$

$R_{A} = R_{C} < R_{B}$