Question

A projectile has a range of 50 m and reaches a maximum height of 10 m. what is the elevation of the projectile?

Answer 1

We know ,

• Horizontal range   $\sf R = \dfrac{u^2sin 2\theta}{g}$   --------------- (1)

• Maximum height   $\sf H = \dfrac{u^2sin^2\theta}{2g}$   --------------- (2)

Dividing (1) by (2) and solving, we get :

$\sf \dfrac{R}{H} = \dfrac{4}{tan\:\theta}$    --------------------- (3)

Given,

• Range (R) = 50 m

• Height (H) = 10 m

Substituting the value in (3), we get :

$\implies\sf \dfrac{50}{10} = \dfrac{4}{tan \:\theta}$

$\implies\sf 5 = \dfrac{4}{tan \:\theta}$

$\implies\sf tan\:\theta = \dfrac{4}{5}$

$\implies\sf \theta = tan^{-1} \:\dfrac{4}{5}$

$\implies\sf \theta = 38.6598 \:degrees$

$\huge\boxed{\rm Elevation\:of\:projectile=38.6598\:\:degrees}$

Answer 2

Solution:-

Given

$\rm \ \: : \implies \: Height(H) = 10m$

$\rm : \implies \: Range (R)\: = 50m$

To find

$\rm \: \to \: elevation \: of \: the \: projectile$

Formula of maximum height

$\rm : \implies \: \boxed{ \rm \: H = \dfrac{ {u}^{2} \sin {}^{2} \alpha }{2g} }$

Formula of Horizontal Range

$\ : \implies \: \boxed{\rm \: R = \dfrac{ {u}^{2} \sin2 \alpha }{g} }$

Put the value of R and H in respective formula

Range

$\ : \implies \: {\rm \: 50 = \dfrac{ {u}^{2} \sin2 \alpha }{g} }$

Heights

$\rm : \implies \: { \rm \: 10= \dfrac{ {u}^{2} \sin {}^{2} \alpha }{2g} }$

Divide Height with range , we get

$: \implies \: \rm \dfrac{10}{50} = \dfrac{ \dfrac{ {u}^{2} \sin {}^{2} \alpha }{2g} }{ \dfrac{ {u}^{2} \sin2 \alpha }{g} }$

Where

$\ : \implies \: \boxed{ \sin2 \alpha = 2 \sin \alpha \cos \alpha }$

we get

$\rm \ \: : \implies \dfrac{1}{5} = \dfrac{ {u}^{2} \sin {}^{2} \alpha }{2g} \times \dfrac{g}{ {u}^{2}2 \sin\alpha \cos \alpha }$

$\rm : \implies \: \dfrac{1}{5} = \dfrac{ \sin \alpha }{4 \cos \alpha }$

$\rm : \implies \dfrac{4}{5} = \dfrac{ \sin \alpha }{ \cos \alpha }$

$\rm : \implies \: \tan \alpha = \dfrac{4}{5}$

so angel of projectile is

$: \implies \boxed{ \alpha = \tan {}^{ - 1} \dfrac{4}{5} }$