Option - C

Let the projected velocity be u and range be R and time taken by the projected body be t1 and t2 with angle .

• As we know in projectile body range is same if the angles is complementary.

Let the angle in first case be and second case be

Time period of projectile is :-

• multiply both equations.

• by arranging the values.

Verified answer

Answer:

3.) t1•t2 = 2R/g

Step by step explanations :

Method 1

Given that,

Maximum range of a projectile at two different angles at the same speed are equal.

We know that,

Maximum Range of a projectile at a vertical angle @

and Maximum range at angle (90 - @ ) are equal

given the time of flight at angle @ = t1

so,

t1 = ([email protected])/g

and time of flight at angle (90 - @) = t2

so,

t2 = 2usin(90 - @) /g

t2 = [email protected]/g

Now,

t1 • t2

([email protected]/g)([email protected]/g)

= (2u² [email protected] [email protected] )/g²

= 2u²[email protected]/g² [[email protected] [email protected] = [email protected]]

= 2R/g

[R = u² [email protected]/g]

so,

t1•t2 = 2R/g

_____________

Method 2

Refer to the attachment