Question

On a certain planet, a small stone tossed vertically upwards at 15m/s takes 7.5 s to return to the ground. What is the acceleration due to gravity on the planet

Answer 1

$<b><u><i> Heya mate!!! Here's your answer</i></u></b>$
______________________________

$\huge{Given -}$

On a planet, when a small stone is tossed vertically upwards at 15 m/s, it takes 7.5 sec to return to the ground.

$\huge{To\: Find}$

Acceleration due to gravity (g) on the planet.

$\huge{Solution}$

$\mathfrak{\green{Firstly,}}$

Initial velocity (u) of the stone = 15 m/s

Time taken (t) = 7.5 sec

Final velocity (v) = 0 m/s (because it will come to rest after returning to the ground)
__________________

$\mathfrak{\green{Now,}}$

We know that, acceleration due to gravity is also a type of acceleration. Hence, g = a(acceleration)

Now, using the first equation of motion, which determines the velocity-time relation, we get that

v = u + at

$\mathcal{Putting\: the\: values}$

=> 0 = 15 + a × 7.5

=> 0 = 15 + 7.5a

=> -7.5a = 15

=> -a = 15/7.5

=> -a = 2

=> a = -2
_________________

Hence, the acceleration due to gravity on the planet (g) = a = -2 m/s², where negative sign shows that the stone is deacclerating or retarding.
_________________

$\mathfrak{\green{Finally,}}$

$\mathcal{Your\: answer\: is}$

$\boxed{\bold{\mathcal{\red{2 \: m/s^2}}}}$
_________________

$\huge{\bold{\mathcal{\blue{Thank\: you}}}}$