A softball is hit over a third baseman’s head with speed v0 and at an angle θ from the horizontal. Immediately after the ball is hit, the third baseman turns around and runs straight back at a constant velocity V = 7.000 m/s, for a time t = 2.000 s. He then catches the ball at the same height at which it left the bat. The third baseman was initially L = 18.00 m from the location where the ball was hit at home plate.
a. Find v0. Use g = 9.807 m/s2 for the magnitude of the acceleration due to gravity.
b. Find the angle θ in degrees.
c. Find a vector expression for the velocity v of the softball 0.1 s before the ball is caught.
d. Find a vector expression for the position r of the softball 0.1 s before the ball is caught.
In: Physics
Suppose there are 2 consumers, A and B. The utility functions of each consumer are given by: UA(X, Y ) = X^1/2 Y^1/2 UB(X, Y ) = 3X + 2Y The initial endowments are: WXA = 10, WYA = 10, WXB = 6, WYB = 6
a) (20 points) Using an Edgeworth Box, graph the initial allocation (label it W) and draw the indifference curve for each consumer that runs through the initial allocation. Be sure to label your graph carefully and accurately.
b) (4 points) What is the marginal rate of substitution for consumer A at the initial allocation?
c) (4 points) What is the MRS for consumer B at the intial allocation?
d) (4 points) Is the initial allocation Pareto efficient? How do you know
In: Economics
Which of the following shocks did NOT contribute to the Great Depression
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rising interest rates |
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stock market crash |
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bank panics |
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rising budget deficits |
Both the Great Recession and the Great Depression
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had unemployment peaking at 10% |
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were caused by short-run aggregate supply shocks |
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were associated with falling prices |
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were associated with a financial crisis |
During the Great Depression, the lack of which safeguard for depositors created the incentive for bank runs?
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Interest rate caps |
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unemployment insurance |
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deposit insurance |
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social security |
When depositors withdraw from the banking system,
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economic activity improves because people spend their money |
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economic activity declines because banks are unable to make loans |
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economic activity is unaffected because banks do not produce goods or services |
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none of the above |
In: Economics
Refer to the Baseball 2016 data, which report information on the 30 Major League Baseball teams for the 2016 season.
In: Statistics and Probability
Refer to the Baseball 2016 data, which report information on the 30 Major League Baseball teams for the 2016 season.
In: Statistics and Probability
At a major food production facility, a cart of bananas with a mass of 200kg is at the top of a 10m high hill, moving with a speed of 6m/s. At the end of the production line is a segment where brakes are applied (uk = 0.4; D = 8m), and then the cart runs into a giant stopping spring (K = 10,000 N/m; total length = 4m).
a. Draw a FBD of the cart while in contact with the spring.
b. Show that the initial energy (at the top of the hill) of the cart is 23,200J.
c. Determine the distance the cart goes after touching the spring before it is brought to rest for the first time (answer to B is Eo).
d. Assuming that, after touching the spring, the cart travels 1.5m (not answer to part C) before stopping, determine the acceleration of the cart at the time its speed is zero.
In: Physics
The accompanying data are the number of wins and the earned run averages (mean number of earned runs allowed per nine innings pitched) for eight baseball pitchers in a recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not.
(a) x=5 wins
(b) x=10 wins
(c) x=21 wins
(d) x=15 wins
Wins, x= 20 18 17 16 14 12 11 9
Earned run average, y= 2.74 3.31 2.65 3.64 3.94 4.34 3.88 5.16
1. Find the regression equation.
In: Statistics and Probability
The accompanying data are the number of wins and the earned run averages (mean number of earned runs allowed per nine inningspitched) for eight baseball pitchers in a recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a) x=5 wins (b) x=10wins (c) x=21 wins (d) x=15 wins
The equation of the regression line is y = (__) x + (__).
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Wins, x |
Earned run average, y |
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20, 2.72
18 3.26
17 2.72
16 3.75
14 3.83
12 4.41
11 3.73
9 5.07
In: Statistics and Probability
Miranda, a satellite of Uranus, is shown in part a of the figure below. It can be modeled as a sphere of radius 242 km and mass 6.68 1019 kg.
(a) Find the free-fall acceleration on its surface. (m/s2)
(b) A cliff on Miranda is 5.00 km high. It appears on the limb at the 11 o'clock position in part a of the figure above and is magnified in part b of the figure above. A devotee of extreme sports runs horizontally off the top of the cliff at 8.50 m/s. For what time interval is he in flight? (Ignore the difference in g between the lip and base of the cliff.) (s)
(c) How far from the base of the vertical cliff does he strike the icy surface of Miranda? m (d) What is his vector impact velocity? (m/s ° below the horizontal)
In: Physics
The length of nylon rope from which a mountain climber is suspended has a force constant of 1.1 × 10^4 N/m.
Part (a) What is the frequency, in Hz, at which he bounces, given his mass and the mass of his equipment is 86 kg?
Part (b) How much would this rope stretch, in centimeters, to break the climber's fall if he free-falls 1.6 m before the rope starts to stretch?
Part (c) What is the frequency, in Hz, at which he bounces, given his mass and the mass of his equipment is 86 kg if the rope is twice as long?
Part (d) How much would this rope stretch, in centimeters, to break the climber's fall if he free-falls 1.6 m before the rope runs out of slack if the rope was twice the length?
In: Physics