A spaceship is moving in an elliptical motion. Their position (x, y) is described by the equation (x^2)/4 + (y-5)^2 = 9 Here, x represents their horizontal position (in km) and y represents the height (in km) of the spaceship: (a) An observer at a certain instant sees the shadow of the spaceship at x = 2 km and observes that the shadow is moving with a speed of 100 km per hour in the positive x direction. The observer also notes that the spaceship is ascending at this instant. How fast is the vertical motion of the spaceship at this instant? Give an exact answer. (b) Assuming that the spaceship doesn’t alter its course, is it moving in a clockewise or counterclockwise motion? (c) The speed of the spaceship is defined by the quantity Square root ((dx/dt)^2 + (dy/dt)^2). What is the speed of the spaceship in Part (a)? You may approximate
A spaceship is moving in an elliptical motion. Their position (x, y) is described by the equation
(x^2)/4 + (y-5)^2 = 9
Here, x represents their horizontal position (in km) and y represents the height (in km) of the spaceship:
(a) An observer at a certain instant sees the shadow of the spaceship at x = 2 km and observes that the shadow is moving with a speed of 100 km per hour in the positive x direction. The observer also notes that the spaceship is ascending at this instant. How fast is the vertical motion of the spaceship at this instant? Give an exact answer.
(b) Assuming that the spaceship doesn’t alter its course, is it moving in a clockewise or counterclockwise motion?
(c) The speed of the spaceship is defined by the quantity Square root ((dx/dt)^2 + (dy/dt)^2). What is the speed of the spaceship in Part (a)? You may approximate
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