A balloon is rising vertically over a point A on the ground a rate of 15 ft/sec. A point B on the ground is level with and 30 ft from A. When the balloon is 40 ft from A, at what rate is its distance from B changing?

Macmillan Learning A planet is in an elliptical orbit around a distant star. At periastron (the point of closest approach to the star), the planet is rp = 3.90 × 108 km from the star and is moving with a speed of Up = 21.5 km/s. When the planet is at apastron (the point of greatest distance from the star), it is ra = 9.00 × 108 km from the star. "P Va = HH How fast is the planet moving at apastron? V km/s

Hello, Can someone please show how to solve this problem? Thanks

Back when I was a kid, I loved to play with my Hot Wheels. Hot Wheels are miniature metal cars that race down lengths of flexible track. The track comes in segments that can be connected together. One thing you can do is make the cars Loop the Loop, as shown in the figure above. Starting at a height, h, the cars race down the track, traverse a circular loop of radius, R, without falling down at the top of the loop, and then continue racing along a section of level track. If the loop is 9 inches in diameter, what is the minimum height, h, from which the cars can start and still loop the loop without falling down at the top? Neglect friction and air resistance.