Answer:
The value of R and the internal resistance of the battery are 10.6 ohm and 2.45 ohm
Explanation:
Given that,
Emf of battery = 15.0 V
Voltage = 12.2 V
Power = 14.0 W
(a). We need to calculate the value of R
Using formula of power



Where, R = resistance
P = power
V = voltage
Put the value into the formula


(b). We need to calculate the internal resistance of the battery
Firstly we calculate the current
Using formula of current

Put the value of P and V into the formula


We calculate the internal resistance
Using formula of emf


Put the value into the formula


Hence, The value of R and the internal resistance of the battery are 10.6 ohm and 2.45 ohm
The total mechanical energy of the system at any time t is the sum of the kinetic energy of motion of the ball and the elastic potential energy stored in the spring:

where m is the mass of the ball, v its speed, k the spring constant and x the displacement of the spring with respect its rest position.
Since it is a harmonic motion, kinetic energy is continuously converted into elastic potential energy and vice-versa.
When the spring is at its maximum displacement, the elastic potential energy is maximum (because the displacement x is maximum) while the kinetic energy is zero (because the velocity of the ball is zero), so in this situation we have:

Instead, when the spring crosses its rest position, the elastic potential energy is zero (because x=0) and therefore the kinetic energy is at maximum (and so, the ball is at its maximum speed):

Since the total energy E is always conserved, the maximum elastic potential energy should be equal to the maximum kinetic energy, and so we can find the value of the maximum speed of the ball:


It hasn't moved from its original spot so displacement is 0
Explanation:
It is given that,
Speed of the ball, v = 10 m/s
Initial position of ball above ground, h = 20 m
(a) Let H is the maximum height reached by the ball. It can be calculated using the conservation of energy as :


h' = 5.1 m
The maximum height above ground,
H = 5.1 + 20
H = 25.1 meters
So, the maximum height reached by the ball is 25.1 meters.
(b) The ball's speed as it passes the window on its way down is same as the initial speed i.e. 10 m/s.
Hence, this is the required solution.