Mechanics> A projectile can have same range for two ...

A projectile can have same range for two angle of projection . If times of flight are t1 and t2 then range of projectile is

Shailesh , 9 Years ago

Grade 11

1 Answers

Paras Verma

assuming x₁and x₂ be those two angle for which range is same and

then, x₂=90-x₁

time of flight =(2usinx)/g

t₁=(2usinx₁)/g

sinx₁=(gt₁)/2u -------(Eqn 1)

t₂=[2usin(90-x₁)]/g

t₂=(2ucosx₁)/g

cosx₁=(gt₂)/2u-------(Eqn 2)

Range=(u²sin2x₁)/g

R=(u²2sinx₁cosx₁)/g

on simplifying

R=(2u²)(sinx₁cosx₁)/g

on substituting from Eqn 1 and Eqn 2

R=(2u²/g)[(gt₁/2u)(gt₂/2u)]

after some hack n slash

R=gt₁t₂/2

taking g=10 (please)

Range=5t₁t₂

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Mechanics> A projectile can have same range for two ...

A projectile can have same range for two angle of projection . If times of flight are t1 and t2 then range of projectile is

Shailesh , 9 Years ago

Paras Verma

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