One stone is dropped from a tower from rest and simultaneously another stone is projected vertically upwards from the tower with some initial velocity. The graph of the distance(s) between the two stones varies with time (t) as (before either stone hits the ground)

Question

One stone is dropped from a tower from rest and simultaneously another stone is projected vertically upwards from the tower with some initial velocity. The graph of the distance(s) between the two stones varies with time (t) as (before either stone hits the ground) (A) Option 1

(B)

(C)

(D)

Tardigrade Admin · Accepted Answer

s1(t)=(1/2) g t2 (downwards) and s2(t)=u t-(1/2) g t2 (upwards) <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-mftedl4s5k5j.png" /> ∴ Distance between the two stones will be s=s1(t)+s2(t)=u t Therefore, s-t graph will be a straight line passing through origin.

Q. One stone is dropped from a tower from rest and simultaneously another stone is projected vertically upwards from the tower with some initial velocity. The graph of the distance(s) between the two stones varies with time $(t)$ as (before either stone hits the ground)

$s_{1} (t) = \frac{1}{2} g t^{2}$ (downwards) and
$s_{2} (t) = u t - \frac{1}{2} g t^{2}$ (upwards)

$∴$ Distance between the two stones will be
$s = s_{1} (t) + s_{2} (t) = u t$
Therefore, $s - t$ graph will be a straight line passing through origin.

Q. One stone is dropped from a tower from rest and simultaneously another stone is projected vertically upwards from the tower with some initial velocity. The graph of the distance(s) between the two stones varies with time (t) as (before either stone hits the ground)

s1​(t)=21​gt2 (downwards) and s2​(t)=ut−21​gt2 (upwards) ∴ Distance between the two stones will be s=s1​(t)+s2​(t)=ut Therefore, s−t graph will be a straight line passing through origin.

Q. One stone is dropped from a tower from rest and simultaneously another stone is projected vertically upwards from the tower with some initial velocity. The graph of the distance(s) between the two stones varies with time $(t)$ as (before either stone hits the ground)

$s_{1} (t) = \frac{1}{2} g t^{2}$ (downwards) and
$s_{2} (t) = u t - \frac{1}{2} g t^{2}$ (upwards)

$∴$ Distance between the two stones will be
$s = s_{1} (t) + s_{2} (t) = u t$
Therefore, $s - t$ graph will be a straight line passing through origin.