Question

02. Two projectiles, one fired from earth with 5ms and
other fired from a planet with 3ms at the same
angle trace identical trajectories. Neglecting friction
what is the acceleration due to gravity on planet
(g = 9.8 ms):​

Answer 1

Answer:

Given:

2 Projectiles have been fired on different planets . The one on Earth is fired at 5 m/s and another one is fired at 3 m/s from another planet.

To find:

To find gravitational acceleration in that planet.

Concept:

Since the question mentions that the trajectories of the Projectile is same , we can say that the Projectiles will have the same range on both planets.

Calculation:

Let gravitational acceleration on the planet be g2.

Ranges are equal ;

$\dfrac{ {(u1)}^{2} \sin(2 \theta) }{g} = \dfrac{ {(u2)}^{2} \sin(2 \theta) }{g2}$

$= > \dfrac{ {(u1)}^{2} }{9.8} = \dfrac{ {(u2)}^{2} }{g2}$

$= > \dfrac{ {5}^{2} }{9.8} = \dfrac{ {3}^{2} }{g2}$

$= > g2 = \dfrac{9 \times 9.8}{25}$

$= > g2 = 3.528 \: m {s}^{ - 2}$

So final answer :

$\boxed{ \red{ \huge{ \bold{ g2 = 3.528 \: m {s}^{ - 2} }}}}$

Answer 2

$</p><p>\huge{\tt{\pink{Hello!!! }}}$

$</p><p>\huge {\fbox{\fbox{\rightarrow{\mathfrak {\green{QUESTION \: : }}}}}}$

Two projectiles, one is fired from earth with 5ms and another one is fired from a planet with 3ms at the same angle trace identical trajectories.

Neglecting friction, what is the acceleration due to gravity on planet.

Take g = 9.8 ms.

$</p><p>\huge {\fbox{\fbox{\rightarrow{\mathfrak {\green{ANSWER\: : 3.528 \: m/s^2 }}}}}}$

These two projectiles trace identical trajectory i.e, their range is same.

$</p><p>\huge{\red{\boxed{\boxed{\mathfrak{R = \frac{u^2 sin(2{\theta})}{g} }}}}}}$

$</p><p>\huge{\red{\boxed{\boxed{\mathfrak{R = \frac{u1^2 sin(2{\theta})}{g} }}}}}} = </p><p>\huge{\red{\boxed{\boxed{\mathfrak{R = \frac{u2^2 sin(2{\theta})}{g} }}}}}} </p><p>$

Let gravitational acceleration on the other planet be g2.

Placing values and equating, we get the value of g2 as 3.528 m/s^2

$</p><p>\huge{\tt{\pink{Hope \: This \: Helps }}}$