Question

which of the following pair of angles with same initial speed hortizontal range is same


30,45
40,45
50,30
40,50 ​

Answer 1

Given:

A few angles have been provided.

To find:

Which pair will have same range ?

Calculation:

ALWAYS REMEMBER THAT : COMPLIMENTARY ANGLES OF PROJECTION (for same velocity of projection) HAVE SAME RANGE .

But how ?

For angle $\theta$

$R = \dfrac{ {u}^{2} \sin(2 \theta) }{g}$

For angle $90^{\circ}-\theta$:

$R = \dfrac{ {u}^{2} \sin \{2 ( {90}^{ \circ} - \theta)\} }{g}$

$\implies R = \dfrac{ {u}^{2} \sin ( {180}^{ \circ} -2 \theta) }{g}$

$\implies R = \dfrac{ {u}^{2} \sin ( 2 \theta) }{g}$

Hence, complimentary angles will have same range !

• 40° and 50° is the correct answer ✔️