A body is under a free fall motion if the only force acting on it is gravity. Near the Earth's surface, the acceleration due to gravity is g = -9.81 m/s. Relaxing beside a lake under a tall tree, you notice a beetle dangling from a tree branch above the lake. You see the beetle fall down and 2 seconds later, hear the water plops. Assuming negligible air resistance, (a) how high is the tree branch from the surface of the lake and (b) what is the speed of the beetle when it hits the lake? You throw a ball upwards with an initial speed of 10 m/s when it has left your hand. Assume negligible air resistance. (a) At what time is the ball 2 m from the position it is released? Hint: use the quadratic formula. (b) Which of these times corresponds to when the ball is going up and when the ball is going down? (c) What is the ball's velocity when it is 1 m from its origin? (d) What is its velocity at the peak of its trajectory?