Respuesta :
Answer:
The distance covered by the rocket after fuel ran out is [tex]3442.04 m[/tex]
Explanation:
Given that the rocket moves with an acceleration [tex]a=30m/s^2[/tex]
time [tex]t=5 s[/tex]
Since the rocket starts from rest initial velocity [tex]u=0 s[/tex]
The distance it travelled within this time is given by [tex]s=ut+ \frac{1}{2} at^2[/tex] [tex]=0 \times 5+ \frac{1}{2} (30\times25)=375 m[/tex]
Velocity at this point is given by [tex]v=u+at[/tex]
[tex]v=0+30\times5=150m/s[/tex]
Given that at this height it runs out of fuel but travels further. Here final velocity [tex]v=0[/tex](maximum height), initial velocity[tex]u=150 m/s[/tex] and time to zero velocity [tex]t=\frac{v}{g} = \frac{150}{9.8} =15.3 s.[/tex]
Thus it travels [tex]15.3 seconds[/tex] more after fuel running out. The distance covered during this period is given
[tex]s= ut+\frac{1}{2} gt^2=150 \times 15.3+1/2 \times9.8 \times 15.3^2=3442.04 m[/tex]
