Question

Two stones are thrown vertically upwards simultaneously from the same point on the ground with initial speeds $u_1=30\text{m/sec}$ and $u_2=50\text{m/sec}$. Which of the curves represents correct variation (for the time interval in which both reach the ground) of
$(x_2-x_1)=$ the relative position of second stone with respect to first with time $\left(t\right)$.
$(v_2-v_1)=$ the relative velocity of second stone with respect to first with time $\left(t\right)$.
Assume that stones do not rebound after hitting the ground

• A. A
• B. B
• C. C
• D. D

Answer 1

Answer: (A), (D)

The correct options are
A A
D D

While both the stones are in flight, $a_1=g$ and $a_2=g$
So $a_{\text{rel}}=0\Rightarrow V_{\text{rel}}=$ constant
$\Rightarrow x_{\text{rel}}=\text{(const)}t$
$\Rightarrow$ Curve of $x_{\text{rel}}$ vs $t$ will be straight line till a stone hits the ground.
After the first particle drops on ground, the separation $\left(x_{\text{rel}}\right)$ will decrease parabolically (due to gravitational acceleration), and finally becomes zero.
and $v_{\text{rel}}=$ slope of $x_{\text{rel}}$ w.r.t. time.