An object is dropped from rest at the height of 150 m, and another object is dropped from rest at a height of100 m. What is the difference in their height after 2 sec if both the object drop with the same acceleration? How does the difference in heights vary with time?

For object A

Initial velocity = u = 0m/s

Height = h = 150m

According to 3^rd equation of motion

v² = u² + 2gh

v² = 0² + 2(9.8)(150)

v² = 19.6 × 150

v² = 2940

v = 54.2m/s

According to 2^nd equation of motion

s = ut + 1/2 gt²

s = 0 + 1/2 (9.8)(2)²

s = (9.8)(2)

s = 19.6m

Distance between object and ground = 150 – 19.6 = 130.4m

For object B

Initial velocity = u = 0m/s

Height = h = 100m

According to 3^rd equation of motion

v² = u² + 2gh

v² = 0² + 2(9.8)(100)

v² = 19.6 × 100

v² = 1960

v = 44.2 m/s

According to 2^nd equation of motion

s = ut + 1/2 gt²

s = 0 + 1/2(9.8)(2)²

s = (9.8)(2)

s = 19.6m

Distance between object and ground = 100 – 19.6 = 80.4m

Distance between the two objects after 2s = 130.4 – 80.4

= 50m