Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed 10 m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first?
(Assume stones do not rebound after hitting the ground and neglect air resistance, take g=10 m/s2)
(The figures are schematic and not drawn to scale.)
The correct option is (C)
We know,
For the first ball,
−240=10t−12gt2
⇒5t2−10t−240
⇒t2−2t−48=0
⇒t=8,−6
The 1st particle will reach the ground in 8 secs.
We know,
For the 2nd particle,
−240=40t−5t2
⇒t2−8t−48=0
t=12secs
The second particle will strike the ground in 12 secs.
Δy=y1−y2=40t−12gt2−10t+12gt2=30t
Δy=30t
After 8 second stone 1 reaches ground
y1=−240m
∴Δy=y2−y1
=40t−12gt2+240
∴ It will be a parabolic curve after 8 secs.
So, correct option is 3.