Final answer:
To find the time it takes for a rocket with constant acceleration to reach a certain altitude, the kinematic equation s = ut + (1/2)at² is used. After substituting known values into the equation, the time is calculated to be 10 seconds, which is answer (b). Option B is correct.
Step-by-step explanation:
The subject of the question is Physics, specifically concerning kinematics and the equations of motion for an object with constant acceleration. The problem describes a rocket accelerating upwards with a constant acceleration. To determine how long it will take the rocket to reach an altitude of 20,000 meters, we use the kinematic equation:
s = ut + (1/2)at²
Where:
s is the distance traveled (20,000 meters)
u is the initial velocity (0 m/s since the rocket starts from rest)
a is the acceleration (400 m/s²)
t is the time which we aim to find
Substituting the known values into the equation gives us:
(1/2) × 400² × t² = 20,000
200² × t² = 20,000
t² = 20,000 / 200
t² = 100
t = √100
t = 10 seconds
The correct answer is (b) 10 seconds.