Question

the range of projectile at 30 degrees is R are at the angle of 60 degree the range will be​

Answer 1

answer: the range is the same for a 15° and a 75° angle. The range is also the same for a 30° and a 60° launch angle.

Explanation:

Answer 2

Answer:

The range of projectile at 30° and 60° will be​ the same, if they are thrown at same speed.

Explanation:

Given the range of projectile at 30° is R.

The range of a projectile is given by

$R=\dfrac{u^{2} sin2\theta}{g}$

where u is the velocity and g is the acceleration due to gravity.

For 30° of projection, the range is

$R=\dfrac{u^{2} sin2\times 30}{g}$

   $=\dfrac{u^{2} sin60}{g}=\dfrac{u^{2} \dfrac{\sqrt{3}}{2} }{g}=\dfrac{u^{2}\sqrt{3} }{2g}$

Now for 60° of projection, the range is

$R=\dfrac{u^{2} sin2\times 60}{g}$

  $=\dfrac{u^{2} sin120}{g}=\dfrac{u^{2} sin(90+30)}{g}=\dfrac{u^{2} cos30}{g}$

  $=\dfrac{u^{2} \dfrac{\sqrt{3}}{2} }{g}=\dfrac{u^{2}\sqrt{3} }{2g}$

As the acceleration due to gravity, g is same in both the cases, and also if the bodies are thrown at same speed at angles 30° and 60°, the range will be same.

The angles 30° and 60° are complementary angles.

So, when the object is thrown at same speed making two different angles so that their sum is 90°, then they have the same range in projectile motion.

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