Two bodies are projected at angle theta and 90 minus theta to the horizontal with the same speed the ratio of their maximum vertical height is?

1 Answer
Mar 13, 2018

the ratio of their maximum height = # (Tantheta )^2 #

Explanation:

As the two bodies are being projected with velocity u
at angle #theta #

and # (90-theta#) respectively ,

their velocity component in vertical direction will be

#u. sin (theta)# and

#u .sin(90-theta) = u cos theta# 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/ (2g) # and

for first body height will be

#h1=( u.sintheta )^2 /(2g) #

and for the second body

#h2 = #(#u cos theta)#) ^2#/(2g) #

so #(h1)/ (h2 )= (Tan Theta)^2#