Question

an aeroplane moving horizontally from west to east with some velocity and with an acceleration 5m/s2 drops a food packet at some instant.then (a) the path of packet is parabolic w.r.t ground

Answer 1

Given:

An aeroplane moving horizontally from west to east with some velocity and with an acceleration 5m/s² drops a food packet at some instant.

To prove:

Path of packet is parabolic with respect to ground.

Proof:

The aeroplane is moving with some velocity and an acceleration of 5 m/s². But after releasing of the packet, the packet will follow a typical "HEIGHT-GROUND" projectile.

Along the X axis , there is no acceleration:

$\therefore \: x = vt$

Along the Y axis , acceleration due to gravity acts downwards.

$\therefore \: y = ut + \dfrac{1}{2} ( - g) {t}^{2}$

$= > \: y = (0 \times t) - \dfrac{1}{2} g {t}^{2}$

$= > \: y = - \dfrac{1}{2} g {t}^{2}$

Putting value of t in this equation:

$= > \: y = - \dfrac{1}{2} \times g \times { (\dfrac{x}{v}) }^{2}$

$= > \: y = - \bigg( \dfrac{g }{2 {v}^{2} } \bigg) {x}^{2}$

So , this is the equation of a parabola with concavity downwards.

Hence , the trajectory of the packet is parabolic with respect to ground.