A ball is thrown directly upward into the air. The graph below shows the vertical position of the ball
with respect to time.
a. How much time does the ball take to reach its
maximum height?
b. How much time does the ball take to reach
one-half its maximum height?
c. Estimate the slope of Ay/At at t = 0.05 s, t =
0.10 s, t= 0.15 s, and t= 0.20 s. On your paper,
draw a coordinate system with velocity (v) on
the y-axis and time (t) on the x-axis. Plot your
velocity estimates against time.

d. From your graph, determine what the acceler-
ation on the ball is.

Which statements about tornadoes are true? check all that apply. (a) about 12,000 tornadoes hit the united states every year. (b) a tornado looks like a funnel. (c) tornadoes are deadly atmospheric storms that cause millions in damages each year. (d) tornadoes can reach wind speeds of more than 300 miles per hour. (e) kansas is the state with the most tornadoes. (f) you will always notice a funnel before a tornado strikes.

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)

Find the dimensions and area of the largest rectangle that can be inscribed in the upper half of the ellipse. (give your answers in terms of a and b. enter the dimensions as a comma-separated list.)