3) when you throw a ball up in the air, the height of the ball is given by the function h(t) = -4.9t2 + vt, where v is the initial speed (in meters per second) with which you threw the ball (we showed this in class). a) prove that the time it takes the ball to reach its maximum height is seconds, and that the total time the ball spends in the air is seconds. 4.9 b) now throw a ball up in the air as hard/fast as you can and with a stop- watch figure out the time the ball spends in the air. then figure out the initial speed with which you threw the ball

Nthe opening scene of the movie raiders of the lost ark, indiana jones replaces a golden statue with a bag of sand. the platform on which the statue is placed is designed to detect the mass of the statue. if the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues. the density of gold is about 20\text{ g/cm}^320 g/cm 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?