Answer:
4.29×10⁵ C
Explanation:
From the question,
The energy stored in the battery = Kinetic energy of the car+ Energy needed to make the car climbed the hill+Energy required to exert a force.
E = 1/2mv²+mgh+Fd.................... Equation 1
Where E = Energy stored in the battery, m = mass of the car, v = velocity of the car, h = height of the hill, F = force exerted on the car, d = distance traveled by the car.
But,
d = vt.................... Equation 2
Where v = velocity, t = time.
Substitute equation 2 into equation 1
E = 1/2mv²+mgh+F(vt)................... Equation 3
Given: m = 770 kg, v = 26 m/s, h = 2.15×10² m = 215 m, F = 5.3×10² N = 530 N, t = 1 hour = 3600 s, g = 9.8 m/s²
Substitute into equation 1
E = 1/2(770)(26²)+(770)(9.8)(215)+(530)(26)(3600)
E = 260260+1622390+49608000
E = 51490650 J
Using,
E = qV................. Equation 4
Where q = charge of the battery, V = Voltage.
make q the subject of the equation
q = E/V............... Equation 5
Given: E = 51490650 J, V = 120 V
Substitute into equation 5
q = 51490650/120
q = 429088.75 C
q = 4.29×10⁵ C
