Question

A stone is dropped into a river from a bridge 125 m above the water. Another stone is thrown vertically down 1.00s after the first is dropped. The stones strike the water at the same time.

Which of these is the correct velocity time graph of both the stones?

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Stone 1 is dropped from height 125, find the time taken

u = 0,a = -10 m/s² , s = -125

$s=ut+\frac{1}{2}a{t}^2$

$-125=0+\frac{1}{2}{t}^2$

t - 5 sec

So stone is graph will be a straight line with constant slope as acceleration is constant. And also the velocity is increasing in negative x-axis.

Now stone 2 was thrown 1 sec later but reached together with stone 1. i.e.,

Time of flight = 4 sec

So

u = ?

a = - 10 m/s

t = 4 sec

s = - 125 m

$-125=u.4+\frac{1}{2}\times (-10)\times 16$

u = 11.25 m/s

So body is starting motion at t = 1 sec with initial velocity of 11.25 m/s downwards and travels till t = 5 sec. The slope of this stone has to be same stone 1 as both the stones have same acceleration