The ratio of heights from which the two different objects fell is [tex]\boxed{1:4}[/tex].
Explanation:
the two identical objects fall from rest. So, it means that the initial velocity of the object as it falls from the height is [tex]0\text{ m/s}[/tex].
The motion of the object as it falls from a height is the motion under the acceleration due to gravity of the earth. The mathematical expression for the distance covered by a object as it falls is:
[tex]\boxed{s=v_{i}t+\dfrac{1}{2}gt^{2}}[/tex] ...... (1)
Here, [tex]s[/tex] is the displacement of the object, [tex]t[/tex] is the time taken, [tex]v_{i}[/tex] is the initial velocity of object and [tex]g[/tex] is the acceleration due to gravity.
The object B takes twice as long as the time taken by the object A to reach the ground. Consider that the object A takes time [tex]t'[/tex] and the object B will take [tex]2t'[/tex] to reach the ground.
Substitute [tex]0 \text{ m/s}[/tex] for the initial velocity of the body.
The ratio of the height from which the objects fall can be obtained as:
[tex]\dfrac{s_A}{s_B}=\dfrac{0+\dfrac{1}{2}g(t')^2}{0+\dfrac{1}{2}g(2t')^2}\\\dfrac{s_A}{s_B}&=\dfrac{1}{4}[/tex]
Therefore, the height from which the object B falls is four times the height from which the object A falls.
Thus, the ratio of heights from which the two different objects fell is [tex]\boxed{1:4}[/tex].
Learn More:
1. Net force acting on the refrigerator https://brainly.com/question/4033012
2. Velocity of the soccer ball during the projectile as it was caught https://brainly.com/question/11023695
3. Unit of the rotational velocity https://brainly.com/question/2887706
Answer Details:
Grade: High School
Subject: Physics
Chapter: Motion in one dimension
Keywords:
two identical object, acceleration due to gravity, twice, time taken to fall, fall through height, ratio of heights, initial velocity, air resistance.
