Free fall problems
Added by Rahmeh A.
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Identify the problem: Understand what the problem is asking. Is it asking for the time it takes for an object to hit the ground, the distance it will fall, the speed it will reach, etc.? Show more…
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Key Concepts
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What is a freely falling body?
For free fall near the surface of a planet where the acceleration due to gravity has a constant magnitude of $g$ length-units/sec', Equation (1) in Exercise 125 takes the form $$ s=-\frac{1}{2} g t^{2}+v_{0} t+s_{0} $$ where $s$ is the body's height above the surface. The equation has a minus sign because the acceleration acts downward, in the direction of decreasing $s$. The velocity $v_{0}$ is positive if the object is rising at time $t=0$ and negative if the object is falling. Instead of using the result of Exercise $125,$ you can derive Equation (2) directly by solving an appropriate initial value problem. What initial value problem? Solve it to be sure you have the right one, explaining the solution steps as you go along.
Applications of Derivatives
Antiderivatives
Free fall near the surface of a planet For free fall near the surface of a planet where the acceleration due to gravity has a constant magnitude of $g$ length-units/ $\sec ^{2},$ Equation $(1)$ in Exercise 99 takes the form $$ s=-\frac{1}{2} g t^{2}+v_{0} t+s_{0} $$ where $s$ is the body's height above the surface. The equation has a minus sign because the acceleration acts downward, in the direction of decreasing $s$ . The velocity $v_{0}$ is positive if the object is rising at time $t=0$ and negative if the object is falling. Instead of using the result of Exercise $99,$ you can derive Equation ( 2$)$ directly by solving an appropriate initial value problem. What initial value problem? Solve it to be sure you have the right one, explaining the solution steps as you go along.
Applications Of Derivatives
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