Question

an object takes 5s to reach the ground from a height of 5 m on a planet . what is the value of g on the planet?
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Answer 1

Given :

▪ Time taken by object to reach the ground from a height (5m) = 5s

To Find :

▪ Gravitational acceleration of the planet.

Concept :

✒ For a body falling freely under the action of gravity, g is taken +ve.

✒ Since, acceleration due to gravity has said to be constant throughout the motion, we can easily apply equation of kinematics to solve this type of questions.

➡ Second equation of kinematics for a freely falling body is given by

$\bigstar\:\underline{\boxed{\bf{\blue{s=\dfrac{1}{2}gt^2}}}}$

Calculation :

• s = 5m
• t = 5m

→ s = (1/2)gt$^2$

→ 2s = gt$^2$

→ 2(5) = g(5×5)

→ 10 = 25g

→ $\underline{\boxed{\bf{\purple{g=0.4\:ms^{-2}}}}}$

✴ Additional information :

• Acceleration due to gravity depends only on mass of planet and radius of planet.
• Acceleration due to gravity doesn't depend on mass of body.

Answer 2

Value of g (gravitational acceleration) = 0.4 m/s²

Solution

Time taken to reach ground (t) = 5 s

Height (h) = 5 m

Initial speed of object (u) = 0 m/s [As it falls freely]

We will use 2nd equation of motion for that :

* 2nd equation → h = ut + ½ gt²

⇒ 5 = 0 × 5 + ½ × g × 5²

⇒ 5 = 0 + ½ × g × 25

⇒ 5 = 12.5g

⇒ g = 5/12.5

⇒ g = 0.4 m/s²

∴ Gravitational acceleration (g) = 0.4 m/s²

_________________________

Equations of motion :

✒ v = u + at [1st equation]

✒ s = ut + ½ at² [2nd equation]

✒ v² - u² = 2as [3rd equation]

For a free falling body,

✒ g = +ve i.e. 10 m/s²

For a vertically up going body,

✒ g = -ve i.e. -10 m/s²