Each shot of the laser gun most favored by rosa the closer, the intrepid vigilante of the lawless 22nd century, is powered by the discharge of a 1.27 f capacitor charged to 59.9 kv . rosa rightly reckons that she can enhance the effect of each laser pulse by increasing the electric potential energy of the charged capacitor. she could do this by replacing the capacitor's filling, whose dielectric constant is 421, with one possessing a dielectric constant of 907.find the electric potential energy of the original capacitor when it is charged.

U = 1794.005 × 10⁶ J

Explanation:

Data provided;

Capacitance of the original capacitor, C = 1.27 F

Potential difference applied to the original capacitor, V = 59.9 kV

= 59.9 × 10³ V

Now,

The Potential energy (U) for the capacitor is calculated as:

Potential energy of the original capacitor, U =  × C × V²

on substituting the respective values, we get

U =  × 1.27 × ( 59.9 × 10³ )²

or

U = 1794.005 × 10⁶ J

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s