For the following exercises, consider a rocket shot into the air that then returns to Earth. The height of the rocket in meters is given by h (t) = 600 + 78.4t – 4.9t², where t is measured in seconds. 20. [T] Compute the average velocity of the rocket over the given time intervals. a. [9, 9.01] b. [8.99, 9] c. [9, 9.001] d. [8.999, 9]
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- Two small spacecraft, each with a mass m = 2000 kg, are in orbit circular Earth, at an altitude h of 400 km. Igor, the commander of one of the ships, arrives at any fixed point in orbit 90 s ahead of Picard, the commander of the other ship. What are the (a) periods T0 and (b) the speed v0 of the ships? At point P, Picard shoots an instantaneous burst in the forward direction, slowing your ship by 1.00%. After this explosion, the elliptical orbit follows, which is shown discontinuous in the figure. What are (c) the kinetic energy and (d) the potential energy of your ship immediately after the explosion? In Picard's new elliptical orbit, what are (e) the total energy E, (f) the semi-major axis a, and (g) the orbital period T? (h) How long before Igor will return Picard to P? Since you can only ansewer to 3 sub-parts, I'll ask here (g, h)I enclose the answer of (f)Two small spacecraft, each with a mass m = 2000 kg, are in orbit circular Earth, at an altitude h of 400 km. Igor, the commander of one of the ships, arrives at any fixed point in orbit 90 s ahead of Picard, the commander of the other ship. What are the (a) periods T0 and (b) the speed v0 of the ships? At point P, Picard shoots an instantaneous burst in the forward direction, slowing your ship by 1.00%. After this explosion, the elliptical orbit follows, which is shown discontinuous in the figure. What are (c) the kinetic energy and (d) the potential energy of your ship immediately after the explosion? In Picard's new elliptical orbit, what are (e) the total energy E, (f) the semi-major axis a, and (g) the orbital period T? (h) How long before Igor will return Picard to P? Since you can only ansewer to 3 sub-parts, I'll ask here (d,e,f)A red train traveling at 72 miles/hour (mph) and a green train traveling at 100 mph are headed toward one another along a straight, level track. When they are 2500 feet apart, each engineer sees the other's train and applies the brakes. The brakes decelerates each train at the rate of 2.0 meters per second squared. Is their a collision? If so, what is the speed of each train at impact? If not, what is the separation between the trains when they stop? Give the given and solution:
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