Question

A ball is projected at an angle of 37° from the
ground. If the same ball is now projected at the
same speed but at an angle of 53°, then the ratio
of their respective horizontal ranges is
(1) 2:1
(2) 1 : 2
(3) 3:5
(4)1:1
​

Answer 1

ANSWER:

OPTION D - 1:1

SOLUTION:

initially the ball is projected with an angle of 37 degree with the horizontal

the horizontal range is is given by the formula,

R = u² sin 2 x / g

we know that,

sin 2 x = 2 sin x .cos x

R = u² 2 sin x .cos x/ g

R = 2 u² 3×4/5×5×g

R = 2 u²×12 /25 g

R = 24 u ² /25 g ..(1)

now the same ball is projected with the same speed but at an angle of 53°

R '= u² sin 2 x / g

R ' = u² 2 sin 53 .cos 53/ g

R '= u² 2 ×4×3/5×5× g

R '= 24 u ² /25 g ..(2)

dividing (1) and( 2) we get

R / R ' = 1

the horizontal range is same for angles x and

90 - x if thier initial velocity is the same