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Monday, November 19, 2012
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Q2:
Question no 02 part a
If coefficient of skewness is zero then distribution is symmetric or zero skewed.\
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question no 2 part b
The least squares regression line
The least squares regression line is the line which produces the smallest value of the sum of the squares of the residuals. A residual is the vertical distance from a point on a scatter diagram to the line of best fit. Therefore the least squares regression line can be seen as the best line of best fit.
The equation of the least squares regression line of y on x is:
Where b is:
As you can see there are 3 different ways to calculate the value for b, based on what information you are given in the question
Example
Calculate the least squared regression line of y on x from the following data:
x
| 20 | 30 | 40 | 50 | 60 | 70 |
y
| 2.49 | 2.41 | 2.38 | 2.14 | 1.97 | 2.03 |
Firstly draw up a table of the values you need and fill it out. In this example we'll use the third equation for b so we need all the values of x2and xiyi:
|
x
|
y
|
x2
|
xiyi
|
| 20 | 2.49 | 400 | 49.9 |
| 30 | 2.41 | 900 | 72.3 |
| 40 | 2.38 | 1600 | 95.2 |
| 50 | 2.14 | 2500 | 107 |
| 60 | 1.97 | 3600 | 118.2 |
| 70 | 2.03 | 4900 | 142.1 |
Sum:
| 270 | 13.42 | 13900 | 584.7 |
Next step is to calculate the means of the x and y values:
Now the value of b can be calculated:
Hence the equation is therefore:
Cleaning it up:
Monday, November 19, 2012
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PHY101 1st Assignment Solution nov 2012
Q 1: A football player kicks a football straight up in to the air with an initial velocity of 25m/s. What is the approximate maximum height that the ball reaches? Use acceleration due to gravity (g) as 9.8m/s2. Marks = 7
Ans:-
2as = Vf2 – Vi2
Where a = g = 9.8m/s2
Vf2 = 0
Applying the values:
2as = Vf2 – Vi2
2(9.8m/s2) s = 0 – (25m/s)2
(19.6m/s2) s = 625m2/s2
s =625m2/s2 / (19.6m/s2)
s = 31.8m
Q 2: In the classic horse and cart problem, a horse is attached to a cart that can roll along on a set of wheels. Which of the following statement is true? Also explain the reason of your selected choice as well.
a) The horse pulls on the cart with a force, and the cart pulls, back on the horse with an equal force.
b) The horse pulls on the cart with a force greater than the force that the cart pulls back on the horse.
c) The horse pulls the cart forward because the force of friction forward is greater than the force of the wagon backward.
d) The horse pulls the cart forward, because of a time delay between the action and reaction forces.
e) The horse pulls the cart forward, but only if the horse has a mass greater than the mass of the cart. Marks = 6 (2+4)
Ans:-
c) The horse pulls the cart forward because the force of friction forward is greater than the force of the wagon backward.
Reason:-
The forces on the cart include the forward force the horse exerts on the cart and the backward force due to friction at the ground, acting on the wheels. At rest, or at constant velocity, these two are equal in size, because the acceleration of the cart is zero. The forces on the horse include the backward force the cart exerts on the horse and the forward force of the ground on its hooves. At rest, or at constant velocity, these two are equal in size, because the acceleration of the horse is zero. The force the horse exerts on the cart is of equal size and opposite direction to the force the cart exerts on the horse, by Newton's third law. The horse places its feet so as to change the angle of the force its hooves exert on the ground, thereby increasing the backward force of its hooves on the ground.
Q 3: Is it true to say that a projectile has zero acceleration at its peak? If yes explain if not give a reason. Marks = 4
Ans:-
The acceleration due to gravity is constant at 9.8 m/sec^2. One of the variables in projectiles is its speed --- it slows down as it goes up and gains speed as it goes down. When the projectile reaches its maximum height, its velocity is always zero. Acceleration has nothing to do with instantaneous velocity. Acceleration shows the relationship between the velocities of the projectile at 2 different points in time. If acceleration was zero, the difference in velocity of the projectiles between any two points of its trajectory would be 0. However, with an acceleration, even if the velocity of the projectile at one point was 0, but the acceleration would not be zero because the acceleration of a projectile is always equal to the acceleration of gravity.
Q 4: (a) Anna is pushing but the box does not move. What is the force of static friction shown in below figure? Marks = 3
Ans:-
Fs=mu*N
=1*7N
=7N
(b) What is the maximum static friction force shown in below figure? The coefficient of static friction for these materials is 0.31. Marks = 5
Ans:-
=0.31*27N
27 nai only 7 hai
or answer hai 2.17
