A ball is tossed into the air with an initial velocity of {{MATH_31}} m/s from a height of 2 meters. When does the ball hit the ground? {{CMD_32}} Knowing that the acceleration due to gravity is {{MATH_33}} m/s{{MATH_34}}, we write {{MATH_35}} Start by taking the antiderivative of both sides of the equation {{ENV_36}} Here {{MATH_37}} represents the initial velocity of the ball. Since it is tossed up with an initial velocity of {{MATH_38}} m/s, {{MATH_39}} and {{MATH_40}} Since the velocity is the derivative of the position, we can write, alternatively {{MATH_41}} Now let's take the antiderivative again. {{ENV_42}} Since we know the initial height was {{MATH_43}} meters, write {{MATH_44}} Hence {{MATH_45}}. We need to know when the ball hits the ground, this is when {{MATH_46}}. Solving the equation {{MATH_47}} we find two solutions {{MATH_48}} and {{MATH_49}}. Discarding the negative solution, we see the ball will hit the ground after approximately {{MATH_50}} seconds. {{CMD_51}} {{CMD_52}}