Question

2 projectile thrown at complementary angles have range of 100m if time of flight of one is 4sec what is the time of flight of another ball?

Answer 1

Answer:

The standard formula for Range of projectile is

R=u2Sin(2α)g  …. eqn 1

Given are two cases where for same speed  u , the two Ranges are equal for two different angles, which happens only when the two throwing angles are  α  and  (90°−α) . What does vary in two cases is the time of flight, which has a relation with the angle of projection. So for each angle, we have a time of flight which can be replaced in the Range formula, as I do here -

Explanation:

T1 = 2uSin(α) / g

T2=2uSin(90°−α) / g

T2=2uCos(α) / g

Taking product of two times of flight

T1T2=2u2(2Sin(α)Cos(α)) / g2

T1T2=2gu2Sin(2α) / g …. eqn 2

Dividing eqn 1 by 2

R / T1T2 = g2

R = T1T2g / 2

Above is just manipulation of formulas observing the standard formulas for R and T are very similar expect one has double angle, which can be obtained using relation between α and  (90°−α) .