Question Sandor fills a bucket with water and whirls it in a vertical circle to demonstrate that the water will not spill from the bucket at the top of the loop. If the length of the rope from his hand to the centre of the bucket is 1.24 m, what is the minimum tension in the rope (at the top of the swing)? How slow can he swing the bucket? Explain your answer. [4]

2. A distributed feedback laser has a Bragg wavelength of 1570nm, a second order grating with A=460nm and a 300 um cavity length. Assuming perfectly symmetrical DFB Laser, find the zeroth, first and second order lasing wavelength .

In the figure m1 = 0.800 kg andm2 = 0.200 kg. The system is released fromrest. What is the distance traveled bym1 after 1.00 s? 86 cm98 cm90 cm94 cm mi S m2

Shelly and Kelly Macdonald met up with Sarah and Tara MacNeill to go fishing in Cape Breton. They found two pools in a stream containing speckled trout (assume equal variance), with the Macdonalds at one pool and the MacNeills at the other, and at the end of the day each team had caught (and released unharmed) 5 fish. For each fish they recorded the length and weight, and the data on length (in cm) is summarized below (Give the answers to 2 places past decimal) Team Macdonald MacNeill Mean 19 Std.Dev 1.6 21.24 2 a.) What is the pooled estimate of the variance? b.) Calculate the 95% confidence interval for the difference in mean length Lower: Upper:

The specific heat of lead is 0.030 cal/g⋅°C. 300 g of lead pellets at 100 °C are mixed with 100 g of water at 70 °C in a thermally insulated container. The final temperature of the mixture isData: specific heat of water = 1 cal/g⋅°CChoose an option:a) 72.5 °Cb)100 °Cc) 74.5°Cd) 85.5 °Ce) 79.5 °C

Garden Sales, Inc., sells garden supplies. Management is planning its cash needs for the second quarter. The company usually has to borrow money during this quarter to support peak sales of lawn care equipment, which occur during May. The following information has been assembled to assist in preparing a cash budget for the quarter: a. Budgeted monthly absorption costing income statements for April-July are: April $ 810,000 567,000 243,000 May $ 950,000 665,000 285,000 June $ 650,000 455,000 195,000 July $ 560,000 392,000 168,000 Sales Cost of goods sold Gross margin Selling and administrative expenses: Selling expense Administrative expense* Total selling and administrative expenses Net operating income 95,000 52,500 147,500 95,500 114,000 74,200 188,200 $ 96,800 76,000 56,000 47,000 53,000 123,000 109,000 $ 72,000 $ 59,000 $ *Includes $37,000 of depreciation each month. b. Sales are 20% for cash and 80% on account. C. Sales on account are collected over a three-month period with 10% collected in the month of sale; 70% collected in the first month following the month of sale; and the remaining 20% collected in the second month following the month of sale. February's sales totaled $305,000, and March's sales totaled $320,000. d. Inventory purchases are paid for within 15 days. Therefore, 50% of a month's inventory purchases are paid for in the month of purchase. The remaining 50% is paid in the following month. Accounts payable at March 31 for inventory purchases during March total $146,300. e. Each month's ending inventory must equal 20% of the cost of the merchandise to be sold in the following month. The merchandise inventory at March 31 is $113,400. f. Dividends of $44,000 will be declared and paid in April. g. Land costing $56,000 will be purchased for cash in May. h. The cash balance at March 31 is $66,000; the company must maintain a cash balance of at least $40,000 at the end of each month. i. The company has an agreement with a local bank that allows the company to borrow in increments of $1,000 at the beginning of each month, up to a total loan balance of $200,000. The interest rate on these loans is 1% per month and for simplicity we will assume that interest is not compounded. The company would, as far as it is able, repay the loan plus accumulated interest at the end of the quarter. Required: 1. Prepare a schedule of expected cash collections for April, May, and June, and for the quarter in total. 2. Prepare the following for merchandise inventory: a. A merchandise purchases budget for April, May, and June. b. A schedule of expected cash disbursements for merchandise purchases for April, May, and June, and for the quarter in total. 3. Prepare a cash budget for April, May, and June as well as in total for the quarter.

how do you solve part c? answer should be 0.187c. 6-2 A particle as observed in a certain reference frame has a total energy of 5 GeV and a momentum of 3 GeV/c (i.e., cp, which has the dimension of energy, is equal to 3 GeV). (a) What is its energy in a frame in which its momentum is equal to 4 GeV/c? (b) What is its rest mass in amu? (c) What is the relative velocity of the two reference frames ?