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The ratio of maximum range to maximum height of a project...

The ratio of maximum range to maximum height of a projectile is 4. Determine the angle of projection.

A.

$30^0$

B.

$60^0$

C.

$45^0$

D.

$0^0$

View answer & explanation

Correct answer is C

Maximum Range R = $\frac{u^2sin2\theta}{g}$

maximum height H = $\frac{u^2sin^2\theta}{2g}$

But R : H = 4

$\frac{u^2sin2\theta}{g}$ : $\frac{u^2sin^2\theta}{2g}$ = 4

$\frac{u^2sin2\theta}{g} \times\frac{2g}{u^2sin^2\theta}$ = 4

$\frac{2sin2\theta}{sin^2\theta}$ = 4

since 2sinΘ = 2sinΘcosΘ

$\frac{2 \times 2sin\theta cos\theta}{sin^2\theta}$ = 4

$\frac{4sin\theta cos\theta}{sin^2\theta}$ = 4

$\frac{sin\theta cos\theta}{sin^2\theta}$ = 1

$\frac{cos\theta}{sin\theta}$ = 1

$\frac{sin\theta}{cos\theta}$ = 1

$tan \theta$ = 1

$\theta = tan^{-1}1$ = 45°

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