Three identical spheres with mass 50-kg are held at the corners of an equilateral triangle 30cm on each side. These spheres are in outer space, far from the influence of any other stars or planets. If one of the spheres is released what will be the magnitude of the initial acceleration of that sphere immediately after the release? a.) 3.7 x 10-8 m/s² b.) 2.5 x 10-8 m/s² c.) 1.9 × 10-8 m/s² d.) 4.2 x 10 m/s² e.) 6.4 x 10 m/s²

1. You and a friend set up an umbrella and chairs at Torrey Pines State Beach. Your friend goes boogie boarding while you read a book. Half an hour later you are surprised to see that your friend has moved south, parallel to the beach. They are still boogie boarding the same distance from shore, in the surf zone. Why did your friend drift parallel to the beach? 2. The Sun is much more massive than the Moon, but the Moon has a bigger influence on Earth's tides than the Sun. Why is this? 3.  Even when there is no wind at the beach, we still see waves. What is the source of these waves? Do not include tides, mass movement, or earthquakes in your answer. 4. What causes ocean surface water to sink to the bottom and become deep water? Where does this happen?  5. How do you escape a Rip Current?

Inside a hemispherical bowl

1. Consider a mass m initially at rest at a large distance I from center of the earth (l>R the earth's radius). The mass m is released and falls toward the earth. (a) Calculate the speed of the mass as a function of its distance x from the center of the earth. (b) In the approximation that l>>R, how much time does it take for the mass m to reach the earth? Express your answers in terms of R, 1, g (acceleration at the earth's surface) and (for part a) x.

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I need help with all parts of this problem. Thank you

V h | "1470-24 g plates A particle of mass m is moving along the +x-axis with constant speed vo. At time t = 0 it enters a region between two plates which are separated by a distance h and lie in the x - z plane as shown in the figure. The figure is a side view of the plates with the +z axis pointing out of the screen. After entering the region between the plates, the particle is acted on by both gravity (which points in the -y direction and has magnitude g) and by a time varying force that points upward, in the +y direction, with magnitude F = bt, where b is a positive constant and is large enough that the particle does not touch the bottom plate. 1. Sketch the trajectory of the particle. 2. How long does it take for the particle to reach its lowest point? 3. If the particle is initially at the midpoint between the two plates, what is the minimum possible value of b such that the particle does not hit the lower plate? 4

14. "Weighing the moon": Knowing the mass of the Earth, ME, Earth-Moon distance, R, and period of moon orbiting around the Barycenter is T. The mass of the Moon can be determined as 47n? R3 (А) Мм GT2 47?R3/2 (B) Мм GT2 4n?R3 (C) Мм – MẸ GT? 4n²R3 (D) MM = MẸ GT2

5) Two neutron stars are separated by a distance of 2.98x10^(10)m. Both have a mass of 3.17x10^(30)kg and a radius of 253000m. They are initially at relative rest. a) What is the speed of both when the distance between them is half the initial value? in m/s b) What is the speed of both when they are about to collide? in m/s

13–131. The rocket is traveling around the earth in free flight along an elliptical orbit AC. If the rocket has the orbit shown, determine the rocket's velocity when it is at point A. *13-132. The rocket is traveling around the earth in free flight along the elliptical orbit AC. Determine its change in speed when it reaches A so that it travels along the elliptical orbit AB. B 8 Mm 8 Mm 10 Mm