Question

Two objects are projected with same velocity ' $u$ ' however at different angles $\propto$ and $\beta$ with the horizontal If $\alpha+\beta=90^{\circ}$, the ratio of horizontal range of the first object to the 2nd object will be :

• A. $1:2$
• B. $4: 1$
• C. $2: 1$
• D. $1:1$

Answer 1

Answer: (D)

$1:1$

Answer 2

The correct answer is (D) : $1:1$
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​