answer:Given: - Helicopter speed relative to the ground: ( v = 5.6 text{ m/s} ) - Helicopter altitude: ( y_0 = 9.5 text{ m} ) - Package's initial velocity relative to the helicopter: ( u = 14.0 text{ m/s} ) - Acceleration due to gravity: ( g = 9.81 text{ m/s}^2 ) a. The initial velocity of the package relative to the ground is the sum of its velocity relative to the helicopter and the helicopter's velocity relative to the ground: [ v_x = u - v = 14.0 text{ m/s} - 5.6 text{ m/s} = 8.4 text{ m/s} ] So, the initial velocity of the package relative to the ground is ( 8.4 text{ m/s} ). b. To find the time it takes for the package to hit the ground, we can use the vertical motion: [ s = y - y_0 = 0 - 9.5 text{ m} ] [ a = -g = -9.81 text{ m/s}^2 ] Using the equation ( s = y_0 + frac{1}{2}at^2 ), we get: [ -9.5 = -4.905t^2 ] [ t^2 = frac{-9.5}{-4.905} ] [ t = 1.39 text{ s} ] The horizontal distance traveled by the package is: [ x = u_xt = 8.4 text{ m/s} times 1.39 text{ s} ] [ x approx 11.96 text{ m} ] The horizontal distance between the helicopter and the package when it hits the ground is approximately ( 11.96 text{ m} ). c. To find the vertical velocity just before impact: [ v_y = -gt = -9.81 text{ m/s}^2 times 1.39 text{ s} ] [ v_y approx -13.63 text{ m/s} ] Now, we can find the angle: [ theta = tan^{-1} left( frac{|v_y|}{v_x} right) = tan^{-1} left( frac{13.63}{8.4} right) ] [ theta approx 58.35^circ ] The angle the package's velocity vector makes with the ground just before impact, as seen from the ground, is ( 58.35^circ ).

answer:From the previous calculation, we know that there are 3 moles of oxygen atoms in 1 mole of SO_3. Therefore, we can use dimensional analysis to find the moles of sulfur: 1.20 x 10^24 O atoms x (1 mol SO_3 / 3 mol O atoms) x (1 mol S / 1 mol SO_3) = 4.00 x 10^23 mol S Therefore, there are 4.00 x 10^23 moles of sulfur in 1.20 x 10^24 oxygen atoms of SO_3.

answer:The smallest RNA molecule is transfer RNA (tRNA). Despite its small size, usually consisting of 70-90 nucleotides, tRNA has a crucial role in the process of protein synthesis within cells. It functions as a link between the genetic information encoded in DNA and the production of proteins. Each tRNA molecule has a distinctive structure that includes an anticodon region and an amino acid attachment site. The anticodon region, based on its nucleotide sequence, matches with a specific codon on the messenger RNA (mRNA). This binding ensures that the correct amino acid is brought to the ribosome, which is the site of protein synthesis. At the amino acid attachment site, the tRNA carries the corresponding amino acid that will be incorporated into the growing polypeptide chain. During protein synthesis, ribosomes read the mRNA's codons, and the complementary tRNA anticodons facilitate the alignment of amino acids. The ribosome then catalyzes the formation of peptide bonds between these amino acids, creating a polypeptide chain according to the genetic code.

answer:To determine the amount of flour needed for each cookie, we need to divide the total amount of flour by the number of cookies. Given that the recipe calls for 2 1/4 cups of flour and yields two dozen cookies, we can calculate as follows: 1. Convert 2 1/4 cups to an improper fraction: 2 1/4 = (2 x 4 + 1) / 4 = 9/4 cups 2. Determine the total number of cookies: Two dozen = 2 x 12 = 24 cookies 3. Divide the total amount of flour by the number of cookies: (9/4 cups) / 24 cookies = 3/32 cups per cookie Therefore, each cookie in the recipe requires 3/32 cups of flour.