Final answer:
The time interval for an object to hit the ground when dropped from a height of 2 km with no initial vertical velocity and acceleration due to gravity of 10 m/s² is 20 seconds. The calculation involves using the kinematic equation for displacement with zero initial velocity.
Step-by-step explanation:
The question is asking for the time interval before an object dropped from an aircraft at a height of 2 km hits the ground, assuming the acceleration due to gravity is 10 m/s². To solve this problem, we can use the kinematic equation for uniformly accelerated motion:
d = vit + (1/2)at²
Where:
- d is the displacement (height from which the object is dropped),
- vi is the initial velocity (since it's dropped and not thrown, this is 0 m/s for the vertical component),
- a is acceleration due to gravity (10 m/s²),
- t is the time in seconds.
Plugging in the known values:
2000 m = 0 * t + (1/2) * (10 m/s²) * t²
This simplifies to:
2000 m = 5t²
t² = 400
t = √400
t = 20 s
The correct answer is (a) 20 s, which is the time it takes for the object to hit the ground.