Question

a. An aircraft is flying horizontally with a velocity of $540km{h}^{-1}$ at a height of $2000$ m from ground. When it is vertically above a point $A$ on the ground, a body is dropped from it. The body reaches the ground at a point $B$. Calculate distance $AB$. Take $g=10m{s}^{-2}$.
b. A stone is dropped from the window of a bus moving at with a velocity $54km{h}^{-1}$ height of window is $245$ cm. Find the distance along the track which the stone covers before striking the ground. Take $g=10m{s}^{-2}$.

Answer 1

$\frac{H}{x}=\tan \theta$

$\Rightarrow h=x\tan \theta$

let the particle reaches at $P$ at time $t$ then.

$h_1=u\sin \theta t-\frac{1}{2}g{t}^2$

Height descended by apple in time $t$].

$h_2=\frac{1}{2}g{t}^2$

$h_1+h_2=u\sin \theta t=u\sin \theta \frac{x}{u\cos \theta }=x\tan \theta =H$

It means the particle will hit the apple.