Question

horizontal range of 37° hundred metre then arrange at 53 degree will​

Answer 1

Let a particle is projected with speed u at an angle $\theta$ with horizontal then,

horizontal range , R = $\frac{u^2sin2\theta}{g}$....(1)

case 1 : $\theta=37^{\circ}$ and R = 100m

from equation (1),

100 = u²sin2(37°)/g

or, 100g = u²sin(74°)

or, u² = 100g/sin(74°) ..... (2)

case 2: $\theta=53^{\circ}$ we have to find R' = ?

so, R' = u²sin2(53°)/g

from equation (2),

R' = 100g/sin(74°) × sin(106°)/g

= {100g/g} × sin(106)/sin(74°)

= 100 × sin(180° - 74°)/sin74°

= 100 × sin74°/sin74°

= 100 m

hence, horizontal range will be 100 when particle is projected at an angle of 53°