Question

The acceleration of a rocket traveling upward is given by a=8+0.02s m/s, where s is in meters. Determine the time needed for the rocket to reach an altitude of $120 m. Initially, s=0.

a) 4 seconds
b) 5 seconds
c) 6 seconds
d) 7 seconds

Answer 1

The time needed for the rocket to reach an altitude of 120 m is approximately 11.54 seconds.

Step-by-step explanation:

To determine the time needed for the rocket to reach an altitude of 120 m, we can use the equation of motion:

v = u + at

Where v is the final velocity, u is the initial velocity (which is 0 here), a is the acceleration, and t is the time. We are given the acceleration as a = 8 + 0.02s m/s, where s is in meters. Since the rocket starts from rest (u = 0), we can set v = 120 m/s and solve for t:

120 = 0 + (8 + 0.02s)t

120 = 8t + 0.02st

120 = (8 + 0.02s)t

t = 120 / (8 + 0.02s)

Substituting s = 120 m into the equation, we get:

t = 120 / (8 + 0.02(120))

t = 120 / (8 + 2.4) = 120 / 10.4

t ≈ 11.54 seconds

Therefore, the time needed for the rocket to reach an altitude of 120 m is approximately 11.54 seconds.