Question

An object is dropped from rest at a height of 150 m and simultaneously another object is dropped from rest at a height 100 m. What is the difference in their heights after 2 s if both the objects drop with same accelerations? How does the difference in heights vary with time?

Answer 1

the square root of height is directly proportional to height.
the difference in height will be 120m - 70m
= 50m

Answer 2

Solution:

Firstly let's calculate distance covered by first object in 2 s. Using second equation of motion ::

$\small\pmb{\boxed{\bf{s = ut + {}^{1}/{}_{2}\:gt^2}}}$

Where, s denotes distance covered, u denotes initial velocity, t denotes time taken, g denotes acceleration due to gravity. We have, u = 0 m/s, g = 10 m/s² and t = 2 s.

★ Putting all values in formula :

↪ s = (0 × 2) + ½ × 10 × (2)²

↪ s = 0 + ½ × 2 × 2 × 10

↪ s = 1 × 2 × 10

↪ s = 2 × 10

➢ s = 20 m

∴ Hence, distance covered by first object in 2 s is 20 m.

Now, let's calculate the distance covered by second object in 2 s by using same formula.

Here, we have u = 0 m/s, g = 10 m/s² and t = 2 s.

★ Putting all values in formula :

↪ s = (0 × 2) + ½ × 10 × (2)²

↪ s = 0 + ½ × 2 × 2 × 10

↪ s = 1 × 2 × 10

↪ s = 2 × 10

➢ s = 20 m

∴ Hence, distance covered by second object in 2 s is 20 m.

Now, let's calculate heights of both objects after 2s :

❏ Calculating height of first object after 2s :

↦ Height of 1st object = 150 - 20

➦ Height of 1st object = 130 m

❏ Calculating height of second object after 2s :

↦ Height of 2nd object = 100 - 20

➦ Height of 2nd object = 80 m

∴ Hence, heights of both objects after 2 s are 130 m and 80m.

Now, let's find difference between their heights, We can easily find it by subtracting height of second object after 2 s from height of first object after 2 s.

❏ Finding difference b/w their heights :

⇒ Difference b/w their heights = 130 - 80

➠ Difference b/w their heights = 50 m

∴ Hence, difference between their heights after 2 s is 50 m.

ㅤ — — — — — — — — — —

We know that initial difference between their heights = 100 - 50 = 50 m and difference between their heights after 2s = 130 - 80 = 50 m. So, both differences are same.

∴ Hence, difference in their height does not vary with time!