1a)A street light is at the top of a 27 ft pole. A 5 ft tall girl walks along a straight path away from the pole with a speed of 3 ft/sec.
At what rate is the tip of her shadow moving away from the light (ie. away from the top of the pole) when the girl is 35 ft away from the pole?
1b) How fast is she going?
2a) A conical water tank with vertex down has a radius of 10 feet at the top and is 21 feet high. If water flows into the tank at a rate of 10 ft^3/min , how fast is the depth of the water increasing when the water is 16 feet deep? The depth of the water is increasing at _______ ft/min.
3a) A kite 75 ft above the ground moves horizontally at a speed of 4 ft/s At what rate is the angle between the string and the horizontal decreasing when 150 ft of string has been let out?
Answer (in radians per second):
4) Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 5.5 mi^2/hr . How rapidly is radius of the spill increasing when the area is 11 mi^2 ? The radius is increasing at _______ mi/hr.
5)The displacement (in meters) of a particle moving in a straight line is given by s=4t^3 where t is measured in seconds. Find the average velocity of the particle over the time interval [9,11] .
Find the (instantaneous) velocity of the particle when t=9 .
6) A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward first base with a speed of 21 ft/s.
At what rate is his distance from second base changing when he is halfway to first base?
Answer =___ ft/s
At what rate is his distance from third base changing at the same moment?
Answer = ___ ft/s
7) If an arrow is shot straight upward on the moon with a velocity of 78 m/s, its height (in meters) after t seconds is given by s(t)= 78t - .83t^2 .
What is the velocity of the arrow (include units) after 5 seconds?
How long will it take for the arrow to return and hit the moon (include units)?
With what velocity (include units) will the arrow hit the moon?