1) The radius of a spherical balloon is increasing at a rate of 3 centimeters pe
ID: 2848586 • Letter: 1
Question
1) The radius of a spherical balloon is increasing at a rate of 3 centimeters per minute. How fast is the volume changing when the radius is 12 centimeters?
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2) The top of a 19 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 2 feet per second. How fast is the bottom of the ladder sliding along the ground when the bottom of the ladder is 8 feet away from the base of the wall?
Answer:
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3) At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 23 knots and ship B is sailing north at 16 knots. How fast (in knots) is the distance between the ships changing at 7 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)
Note: Draw yourself a diagram which shows where the ships are at noon and where they are "some time" later on. You will need to use geometry to work out a formula which tells you how far apart the ships are at time t, and you will need to use "distance = velocity * time" to work out how far the ships have travelled after time t.
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Explanation / Answer
1) 5427.6 cm^3/min
2) 4.308 ft/sec
3) 28 knots
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