Question

A projectile has the same range R when the maximum height attained by it is either H1 or H2 .find the relation between R , H1 amd H2.

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Answer 1

see,there are two projectiles,

(1) range 'R' and height 'H1'

(2) range'R' and height 'H2'

(1) R=u^2sin2@/g=u^2.2sin@cos@/g and H1(max)=u^2/2g

relation between R and H1;

dividing R/H1,

R/H1=u^2.2sin@cos@/g.2g/u^2=4sin@cos@

R=H1.4sin@cos@

R=H1.2.sin2@

(2)R=u^2sin2@/g=u^2.2sin@cos@/g and H2(max)=u^2/2g

relation between R and H2;

dividing R/H2,

R/H2=u^2.2sin@cos@/g.2g/u^2=4sin@cos@

R=H2.4sin@cos@

R=H2.2.sin2@

relation between H1 and H2;

H1.2.sin2@=H2.2.sin2@

H1=H2

[@=theta, sin2@=2sin@cos@]

........ I hope you will understand and like the answer.