Two objects are projected with same velocity ' u ' however at different angles propto and β with the horizontal. If α+β=90°, the ratio of horizontal range of the first object to the 2 textnd object will be :

Question

Two objects are projected with same velocity ' u ' however at different angles propto and β with the horizontal. If α+β=90°, the ratio of horizontal range of the first object to the 2 textnd object will be : (A) 1:2 (B) 4: 1 (C) 2: 1 (D) 1:1

Tardigrade Admin · Accepted Answer

text Range =( u 2 sin 2 θ/ g ) Range for projection angle " α " R 1=( u 2 sin 2 α/ g ) Range for projection angle " β " R 2=( u 2 sin 2 β/ g ) α+β=90° text (Given) ⇒ β=90°-α R 2=( u 2 sin 2(90°-α)/ g ) R 2=( u 2 sin (180°-2 α)/ g ) R 2=( u 2 sin 2 α/ g ) ⇒ ( R 1/ R 2)=((( u 2 sin 2 α/ g ))/(( u 2 sin 2 α) g ))=(1/1)

Q. Two objects are projected with same velocity ' $u$ ' however at different angles $\propto$ and $β$ with the horizontal. If $α + β = 9 0^{\circ}$ , the ratio of horizontal range of the first object to the $2^{nd}$ object will be :

$1 : 2$

$4 : 1$

$2 : 1$

$1 : 1$

Q. Two objects are projected with same velocity ' u ' however at different angles ∝ and β with the horizontal. If α+β=90∘, the ratio of horizontal range of the first object to the 2nd object will be :

1:2

4:1

2:1

1:1

Range =gu2sin2θ​ Range for projection angle " α " R1​=gu2sin2α​ Range for projection angle " β " R2​=gu2sin2β​ α+β=90∘ (Given) ⇒β=90∘−α R2​=gu2sin2(90∘−α)​ R2​=gu2sin(180∘−2α)​ R2​=gu2sin2α​ ⇒R2​R1​​=(gu2sin2α​)(gu2sin2α​)​=11​

Q. Two objects are projected with same velocity ' $u$ ' however at different angles $\propto$ and $β$ with the horizontal. If $α + β = 9 0^{\circ}$ , the ratio of horizontal range of the first object to the $2^{nd}$ object will be :

$1 : 2$

$4 : 1$

$2 : 1$

$1 : 1$