Answer :
Answer:
The total distance traveled by body is = 274.41 m
Explanation:
Given :
Combined mass [tex]m = 75[/tex] Kg
Thrust force [tex]F_{t} =[/tex] 200 N
Coefficient of kinetic friction [tex]\mu _{k} =[/tex] 0.10
According to newton's law
[tex]F_{t} - \mu m g = ma[/tex]
[tex]200 - 0.1 \times 75 \times 9.8 = 75 a[/tex] ( ∵ [tex]g = 9.8 \frac{m}{s^{2} }[/tex] )
Before run out of fuel the acceleration is,
[tex]a = \frac{126.43}{75} = 1.69\frac{m}{s^{2} }[/tex]
Distance covered in 11 sec. is given by,
[tex]y = v_{0}t + \frac{1}{2}at^{2}[/tex]
Where [tex]y =[/tex] distance, [tex]v_{0} =[/tex] initial velocity = [tex]0[/tex], [tex]a =[/tex] acceleration,
[tex]y = \frac{1}{2} \times 1.69 \times (11) ^{2}[/tex]
[tex]y = 102.24[/tex] m
After run out of fuel velocity of body is,
[tex]v = v_{o} + at[/tex]
Where [tex]v_{o} =[/tex] 0
[tex]v = 1.69 \times 11 = 18.37 \frac{m}{s}[/tex]
After fuel run out of only frictional force act on body,
[tex]ma = \mu_{k} m g[/tex]
Acceleration is given by,
[tex]a = 0.1 \times 9.8[/tex]
[tex]a = 0.98 \frac{m}{s^{2} }[/tex]
So distance traveled by body after run out of fuel is given by
[tex]v^{2} - v_{o} ^{2} =2ax[/tex]
Where initial velocity [tex]v_{o} =[/tex] 0,
[tex]x = \frac{337.46}{1.96}[/tex]
[tex]x = 172.17[/tex] m
So total distance traveled by body is,
[tex]d = 172.17 +102.24 = 274.41[/tex] m