You are a stunt person in the latest action movie and need to drive a car off a cliff, parachute out to safety, and let the car freefall to the bottom of the cliff. You must leave the cliff at a specific speed, so the car lands on the target below. You start from rest, hit the gas, and accelerate at a constant rate of 11 m/s2 for 7.5 seconds, when you realize you are going too fast. You apply the brakes for 5 seconds, slowing your car down with a constant acceleration of -4.5 m/s2 . The car leaves the cliff traveling horizontally, you parachute out, and the car hits the target 30 meters below. How far from the cliff is the

Lake happy times contains 100 km3 of pure water. it is fed by a river at a rate of 50 km3/yr. at time zero, there is a factory on one shore of lake happy times that begins introducing a pollutant to the lake at a rate of 2km3/yr. there is another river that is fed by lake happy times at a rate that keeps the volume of lake happy times constant. this means that the rate of flow from lake happy times into the outlet river is 52km3/yr. in turn, the flow from this outlet river goes into another lake, lake sad times, at an equal rate. finally, there is an outlet river from lake sad times flowing at a rate that keeps the volume of lake sad times at a constant 100 km3 . (a) find the amount of pollutant in lake sad times at the end of 3 months. (b) at the end of 3 months, observers close the factory due to environmental concerns and no further pollu- tant enters lake happy times. how long will it take for the pollutant in lake sad times (found in part (a)) to be cut in half?