Answer:
The Length of the driveway is 4.98 m
Explanation:
we have to determine the length of the driveway
so we use following equations
W=ΔK.E where W is work and ΔK.E change in the kinetic energy
also
[tex]K.E = \frac{ MV^2}{2}[/tex]
also
W = F.d Where F is Force and d is distance
Given that
[tex]F_{f}[/tex]= 4000 N this frictional force
m = 2100 Kg
θ= 20.0°
V=3.8 m/s V is the car's speed at the bottom of the driveway
W=Δ K.E
[tex]W = (1/2)(2100)(3.8)^2[/tex] = 15162 J
Since the x component of the gravity is
[tex]Fx_[/tex] = mg sinФ
so
[tex]Fx_{}[/tex] = (2100)(9.8)sin(20.0° ) we get
[tex]Fx_{}[/tex] = 7038.77 N
And the Net force is
[tex]F_{net}[/tex] = [tex]Fx_ {}[/tex] - [tex]F_{f}[/tex]
[tex]F_{net}[/tex] = 7038.77 - 4000 = 3038.77 N
And the length of the driveway = W / ([tex]F_{net}[/tex] ) = 15162/3038.77 = 4.98 m
So this the length of the driveway.
The length of the driveway for the given car is 5.0 m.
The net horizontal force on the car is calculated as follows;
[tex]F_{net} = mg\ sin(\theta) \ - \ F_f\\\\F_{net} = (2.1 \times 10^3 \times 9.8 \times sin(20)) \ - \ (4,000)\\\\F_{net} = 3038.78 \ N[/tex]
The kinetic energy of the car at the bottom of the driveway is calculated as follows;
[tex]K.E = \frac{1}{2} mv^2\\\\K.E = \frac{1}{2} \times 2,100 \times (3.8)^2\\\\K.E = 15,162 \ J[/tex]
Apply work-energy theorem to determine the length of the driveway as follows;
[tex]F_x d = K.E\\\\d = \frac{15,162}{3038.78} \\\\d = 5.0 \ m[/tex]
Thus, the length of the driveway for the given car is 5.0 m.
Learn more about work-energy theorem here: https://brainly.com/question/10063455
