Abaseball, hit 7 feet above the ground, leaves the bat at an angle of 55 ° and is caught by an outfielder 6 feet above the ground and 48 feet from home plate. neglecting air resistance, what was the initial speed of the ball? use g = 32 ft/sec2 as the acceleration of gravity. your answer should be in feet per second.

In raising a 6200-n piano with a pulley system, the movers note that, for every 2.2 m of rope pulled down, the piano rises 0.12 m . ideally, find the force required to lift the piano.

Atank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. the values in the table show the volume v of water remaining in the tank (in gallons) after t minutes.t(min) 5 10 15 20 25 30v(gal) 694 444 250 111 28 0(a) if p is the point (15, 250) on the graph of v, find the slopes of the secant lines pq when q is the point on the graph with t = 5, 10, 20, 25, and 30.(b) estimate the slope of the tangent line at p by averaging the slopes of two secant lines.(c) use a graph of the function to estimate the slope of the tangent line at p. (this slope represents the rate at which the water is flowing from the tank after 15 minutes.)show all steps.

If an athlete runs once around a track, back to the starting line, her average velocity is zero. true or false?