Flag Most Scoring Topics in IIT JEE> A stone is dropped from the top of a tall...
question mark

A stone is dropped from the top of a tall cliff and `n` seconds later another stone is thrown vertically downwards with velocity `u`. Then the second stone overtakes the first, below the top of cliff at a distance given by :

Sagar , 7 Years ago
Grade 12th pass
anser 2 Answers
Rahul G

Last Activity: 7 Years ago

taking +ve axis along downward direction of pillar , equation of first stone is y= \frac{1}{2}gt^{2}
                                                                                 
equation of second is  y=u(t-n)+ \frac{1}{2}g(t-n)^{2} can be verified that if t=n then y=0 therefore stone is still at origin .
now solving the two equations we get t=\frac{ng}{u}[1-\frac{n}{2}]+n
and substituting value of t in first we get y=\frac{1}{2}g[\frac{ng}{u}(1-\frac{n}{2})+n]^{2} which is the point of intersection of two stones in terms of given and also the point where stone two overtakes stone 1

Vipul Tiwari

Last Activity: 7 Years ago

let time taken by first stone be ts and that of the other stone be (t-n)s
so,distance travelled by first stone is :
s=1/2(gt^2)..........eq^n(1)
and that of the other stone is :
s=u(t-n) + 1/2[g(t-n)^2].........eq^n(2)
since both the stones meet at the distance so eq^n(1) and eq^n(2) will be equal
1/2gt^2=u(t-n) + 1/2[g(t-n)^2]
gt^2 = 2ut-2un + gt^2 + gn^2 -2gnt
t(2gn-2u) = gn^2-2un
t =(gn^2-2un)/(2gn-2u)
t=n(gn/2 – u)/(gn-u)
now putting value of t in eq^n(1)
s=1/2[g{n(gn/2 – u)/(gn-u)}^2]
s=g/2[n(gn/2 – u)/(gn-u)^2]

Provide a better Answer & Earn Cool Goodies

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free