Answer:
The internal resistance of the cell is 0.051 ohm.
Explanation:
Given;
emf of the battery, E = 12 V
terminal voltage of the cell, V = 8.2 V
current in the circuit, I = 75 A
let the potential drop of the cell due to internal resistance (r) = Ir
The internal resistance of the cell is calculated from the equation below;
E = V + Ir
where;
r is the internal resistance of the cell

Therefore, the internal resistance of the cell is 0.051 ohm.
The average velocity is -4.17 m/s
Explanation:
The average velocity of a body is given by:

where
d is the displacement of the body
t is the time elapsed
For the student in this problem, we have:
Initial position: 
Final position: 
So the displacement is

The time elapsed is
t = 60 s
Therefore, the average velocity is

Where the negative sign means the student is moving towards the origin.
Learn more about average speed and velocity:
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Answer:
T= 4.24sec
Explanation:
We are going to use the formula below to calculate.

Where T is period
L is length of rod
g is acceleration due to gravity =
From the problem, the rod is pivoted at 1/4L which means that three quarter of the rod was used for the oscillation. lets call this

= 4.4625m
thus
T= 4.24sec
To find average speed, we divide the distance of travel (in this case, 400 metres) by the time she took, 32 seconds. Therefore: 12.5 seconds is her average speed.
A projectile motion is characterized by a motion whose path is alike to that of an arc. It already has its derived equations. For the maximum height H and the maximum range R, the equations are:
H = v₀²sin²θ/2g ; R = v₀²sin(2θ)/g
As you can observe, they are almost alike. Since they both contain v₀²/g, let's isolate this term for both equations:
v₀²/g = 2H/sin²θ
v₀²/g = R/sin (2θ)
Equating both equations:
2H/sin²θ = R/sin (2θ)
H = Rsin²θ/2sin(2θ)
This is the equation that relates H to R.