Question

Two projectiles A and B are thrown from the same point with velocities v and v/2 respectively. If B is thrown at an angle 45°with horizontal ,what is the inclination of A when their ranges are the same?

Answer 1

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Answer 2

Given that,

Velocity of A $v_{A}= v$

Velocity of B$v_{B} =\dfrac{v}{2}$

Angle $\theta_{B}= 45^{\circ}$

We need to calculate the range for A

Using formula of range

$R_{A}=\dfrac{v^2\sin2\theta}{g}$

Put the value into the formula

$R_{A}=\dfrac{v^2\sin2\theta}{g}$

We need to calculate the range for B

Using formula of range

$R_{B}=\dfrac{v^2\sin2\theta}{g}$

Put the value into the formula

$R_{B}=\dfrac{v^2\sin90}{4g}$

$R_{B}=\dfrac{v^2}{4g}$

When their ranges are the same,

We need to calculate the angle

Using formula of range

$R_{A}=R_{B}$

Put the value into the formula

$\dfrac{v^2\sin2\theta}{g}=\dfrac{v^2}{4g}$

$\sin2\theta=\dfrac{1}{4}$

$\theta=\dfrac{1}{2}\sin^{-1}(\dfrac{1}{4})$

$\theta=7.23^{\circ}$

Hence, The inclination of A is 7.23°.