Question

The horizontal ranges described by two projectiles, projected at angles $({45}^{\circ }-\theta )$ and $({45}^{\circ }+\theta )$ from the same point and same velocity are in the ratio.

• A. $2:1$
• B. $1:1$
• C. $2:3$
• D. $1:2$

Answer 1

The correct option is B $1:1$

$Thehorizontalrangeofthecomplementaryangleofprojectionalwaysremainssame.Andgivenprojectedangles=({45}^0+\theta )and({45}^0-\theta )whicharecomplementarytoeachother.Thusratiooftheprojectangles=\frac{u^{2}sin2({45}^0-\theta )}{u^{2}sin2({45}^0+\theta )}=\frac{sin({90}^0-\theta )}{sin({90}^0+\theta )}=\frac{cos2\theta }{cos2\theta }=1uandggetscancelout.$