A body Falls freely under gravity starting from rest. Find the ratio o...
Answer
When a body falls freely under gravity starting from rest, it follows a motion known as free fall. The distance travelled by the body during different intervals of time can be calculated using the equations of motion.
Calculating distance travelled during the first half of the interval of time
Let's assume that the body falls for a time t. During the first half of this time, the body covers a distance d1. We can calculate d1 using the first equation of motion:
d1 = (1/2)gt^2
where g is the acceleration due to gravity (9.8 m/s^2).
Calculating distance travelled during any interval of time
During any interval of time, the body covers a distance d. We can calculate d using the second equation of motion:
d = (1/2)gt^2
Calculating distance travelled during the second half of the interval of time
During the second half of the time, the body covers a distance d2. We can calculate d2 using the third equation of motion:
d2 = d - d1 = (1/2)gt^2 - (1/2)gt^2/2 = (1/4)gt^2
Ratio of distance travelled during the first half to the distance travelled during the second half
We can calculate the ratio of distance travelled during the first half to the distance travelled during the second half by dividing d1 by d2:
d1/d2 = [(1/2)gt^2]/[(1/4)gt^2] = 2
Therefore, the ratio of distance travelled by the body during the first half to the distance travelled during the second half of the same interval of time is 2.