Answer:
3.28 m
3.28 s
Explanation:
We can adopt a system of reference with an axis along the incline, the origin being at the position of the girl and the positive X axis going up slope.
Then we know that the ball is subject to a constant acceleration of 0.25*g (2.45 m/s^2) pointing down slope. Since the acceleration is constant we can use the equation for constant acceleration:
X(t) = X0 + V0 * t + 1/2 * a * t^2
X0 = 0
V0 = 4 m/s
a = -2.45 m/s^2 (because the acceleration is down slope)
Then:
X(t) = 4*t - 1.22*t^2
And the equation for speed is:
V(t) = V0 + a * t
V(t) = 4 - 2.45 * t
If we equate this to zero we can find the moment where it stops and begins rolling down, that will be the highest point:
0 = 4 - 2.45 * t
4 = 2.45 * t
t = 1.63 s
Replacing that time on the position equation:
X(1.63) = 4 * 1.63 - 1.22 * 1.63^2 = 3.28 m
To find the time it will take to return we equate the position equation to zero:
0 = 4 * t - 1.22 * t^2
Since this is a quadratic equation it will have to answers, one will be the moment the ball was released (t = 0), the other will eb the moment when it returns:
0 = t * (4 - 1.22*t)
t1 = 0
0 = 4 - 1.22*t2
1.22 * t2 = 4
t2 = 3.28 s
Answer:
Explanation:
Those kind of problems of electric physics is about capacitors, so the normal questions are:
What are the charge on each electrode?
Solve this you can get other information required in the problem or write down the other questions you need
Capacitance
The charge is find by the equation
Answer:
0.0002 C.
Explanation:
Charge: This can be defined as the ratio of current to time flowing in a circuit. The S.I unit of charge is Coulombs (C)
Mathematically, charge can be expressed as
Q = CV ................................. Equation 1
Where Q = amount of charge, C = capacitance of the capacitor, V = potential difference across the plates.
Given: C = 2.0-μF = 2×10⁻⁶ F, V = 100 V.
Substitute into equation 1
Q = 2×10⁻⁶× 100
Q = 2×10⁻⁴ C
Q = 0.0002 C.
The amount of charge accumulated = 0.0002 C
Answer:
(a) k = 
(b) τ = 
∝
Explanation:
The moment of parallel pipe rotating about it's axis is given by the formula;
I = ---------------------------------1
(a) The kinetic energy of a parallel pipe is also given as;
k =
--------------------------------2
Putting equation 1 into equation 2, we have;
k = 
k =
(b) The angular momentum is given by the formula;
τ = Iw -----------------------3
Putting equation 1 into equation 3, we have
τ = 
But
τ = dτ/dt = 
------------------4
where
dw/dt = angular acceleration =∝
Equation 4 becomes;
τ = ∝
The big bang produced dark energy, which accounts for some of the energy needed to expand the universe.
The vastness of space may contain a type of matter known as “dark matter.”
The universe is currently expanding at an accelerating rate.
Hope this helps !
