Question

A projectile has a time of flight T & range R. If time of flight is doubled keeping angle of projection same, then what will be the new range?

Answer 1

range will be four times, which means range is directly proportional to square of time .

Answer 2

T = Original time.
T' = Final time.
R = Original range.
R' = Final range.

As per given condition,
T = 2T'
2usin∅/g = 2(2u'sin∅/g)
u = 2u'

R = u²sin2∅/g
R' = u'²sin2∅/g

R/R' = u²/u'²
R/R' = 4u'²/u'²
R/R' = 4
R' = R/4

Hence, the new range will be one-fourth of the original.