Question

Suppose a rocket ship in deep space moves with constant acceleration equal to 9.80 m/s2, which gives the illusion of normal gravity during the flight. (a) If it starts from rest, how long will it take to acquire a speed 12% that of light, which travels at 3.0 × 108 m/s? (b) How far will it travel in so doing?

Answer 1

a) 3673469.39 seconds

b) 6.61×10¹⁴ m

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity = 0.12×3×10⁸ m/s

s = Displacement

a = Acceleration due to gravity = 9.8 m/s²

Equation of motion

`v=u+at\\\Rightarrow 0.12* 3* 10^8=0+9.8t\\\Rightarrow t=(0.12* 3* 10^8)/(9.8)=3673469.39\ s`

Time taken to reach 12% of light speed is 3673469.39 seconds

`v^2-u^2=2as\\\Rightarrow s=(v^2-u^2)/(2a)\\\Rightarrow s=((0.12* 3* 10^8)^2-0^2)/(2* 9.8)\\\Rightarrow s=6.61 * 10^(14)\ m`

The distance it would have to travel is 6.61×10¹⁴ m