Question

The acceleration of free fall on a certain planet is 8.0 m s-2. An object gets dropped from a

height and hits the ground after 1.5 s. From what height must the object have been dropped?

Answer 1

• Height from which the object is dropped is 9m

We are given that:

• The acceleration of free fall on a certain planet is 8m/s². An object is dropped from the height and hits the ground after 1.5s

We need to find:

• Height from which the object was dropped.

Using equations of motion:

➙ v² - u² = 2as

➙ v = u + at

here,

• u = initial velocity

• v = final velocity

• a = acceleration

• s = displacement

• t = time taken

Solution:

From the given information, we can conclude that:

• initial velocity of the object is 0 m/s

• acceleration due to gravity = 8 m/s²

• time taken = 1.5 seconds

Now, using equation of motion:

➝ v = u + at

➝ v = 0 + ( 8 × 1.5 )

➝ v = 0 + 12 .0

➝ v = 12 m/s

• final velocity of object = 12 m/s

For, acceleration :

➝ v² - u² = 2as

➝ ( 12 )² - ( 0 )² = 2 × 8 × s

➝ 144 - 0 = 16s

➝ 16 s = 144

➝ s = 144 / 16

➝ s = 9m

• Displacement = 9 m

`\dag` Since, we take displacement in terms of distance in some places, therefore we can say that the height from which the object was dropped is 9 meters .