Question

Two bodies are projected at angles θ and (90∘−θ) with the horizontal at the same speed.The ratio of their maximum heights is

Answer 1

Answer:

the ratio of their maximum height =  

(

tan

θ

)

2

Explanation:

As the two bodies are being projected with velocity u  

at angle  

θ

and  

(

90

−

θ

) respectively ,

their velocity component in vertical direction will be

u

.

sin

(

θ

)

and

u

.

sin

(

90

−

θ

)

=

u

cos

θ

respectively.

At the maximum height the final velocity (v) in vertical

direction will be zero for both bodies.

Therefore

using the relation between u, v and

the distance traversed h one can write -

v

2

=

u

2

−

2

.

g

.

h

in which v=0 ; We get

h

=

u

2

2

g

and

for first body height will be

h

1

=

(

u

.

sin

θ

)

2

2

g

and for the second body

h

2

=

(

u

cos

θ

)

) ^2

/

(

2

g

)

so  

h

1

h

2

=

(

tan

Θ

)

2