If an apple has a mass of {{MATH_27}} and it is dropped from a height of {{MATH_28}}, how much energy is released when it hits the ground? Assume that the acceleration due to gravity is {{MATH_29}}. {{CMD_30}} First we need to find the velocity at which the apple hits the ground. Let {{MATH_31}} represent acceleration at time {{MATH_32}} and {{MATH_33}} represent velocity. Since {{MATH_34}}, we know that {{ENV_35}} Now we need to know how long it takes for the apple to hit the ground, after being dropped from a height of {{MATH_36}} meter. For this we'll need a formula for position. Here {{MATH_37}}, so we'll need to use an indefinite integral: {{ENV_38}} Since {{MATH_39}}, write with me {{MATH_40}} hence {{MATH_41}} and {{MATH_42}}. Solving the equation {{MATH_43}} for {{MATH_44}} tells us the time the apple hits the ground. Write with me {{ENV_45}} So the apple hits the ground after {{MATH_46}} seconds. Finally, the formula for kinetic energy is {{ENV_47}} Ah! So the kinetic energy released by an apple dropped from a height of {{MATH_48}} meter is approximately {{MATH_49}} joule. {{CMD_50}} {{CMD_51}}