Motion in a Plane · Question 17

Two projectiles are fired with same initial speed from same point on ground at angles of (45 - ) and (45 + ), respectively, with the horizontal direction. The ratio of their maximum heights attained is :

1. 1+ 1-
2. 1+ 2 1- 2
3. 1- 1+
4. 1- 2 1+ 2

Answer

(4) 1- 2 1+ 2

Solution

Maximum height: H = u2 2 2g, so for the same u, H 2

H1H2 = 2(45 - ) 2(45 + )

Using 2 2 = 1- 2 :

H1H2 = 1- (90 -2 )1- (90 +2 )

H1H2 = 1- 2 1+ 2

Answer: (4)