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Visit this site to learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms (for example, y = bx ) to see how they add to generate the polynomial curve.
What is the acceleration of a rock thrown straight upward on the way up? At the top of its flight? On the way down? Assume there is no air resistance.
An object that is thrown straight up falls back to Earth. This is one-dimensional motion. (a) When is its velocity zero? (b) Does its velocity change direction? (c) Does the acceleration have the same sign on the way up as on the way down?
a. at the top of its trajectory; b. yes, at the top of its trajectory; c. yes
Suppose you throw a rock nearly straight up at a coconut in a palm tree and the rock just misses the coconut on the way up but hits the coconut on the way down. Neglecting air resistance and the slight horizontal variation in motion to account for the hit and miss of the coconut, how does the speed of the rock when it hits the coconut on the way down compare with what it would have been if it had hit the coconut on the way up? Is it more likely to dislodge the coconut on the way up or down? Explain.
The severity of a fall depends on your speed when you strike the ground. All factors but the acceleration from gravity being the same, how many times higher could a safe fall on the Moon than on Earth (gravitational acceleration on the Moon is about one-sixth that of the Earth)?
Earth $v={v}_{0}-gt=\text{\u2212}gt$ ; Moon ${v}^{\prime}=\frac{g}{6}{t}^{\prime}\phantom{\rule{0.5em}{0ex}}v={v}^{\prime}\phantom{\rule{0.5em}{0ex}}-gt=-\frac{g}{6}{t}^{\prime}\phantom{\rule{0.5em}{0ex}}{t}^{\prime}=6t$ ; Earth $y=-\frac{1}{2}g{t}^{2}$ Moon ${y}^{\prime}=-\frac{1}{2}\phantom{\rule{0.2em}{0ex}}\frac{g}{6}{(6t)}^{2}=-\frac{1}{2}g6{t}^{2}=\mathrm{-6}\left(\frac{1}{2}g{t}^{2}\right)=\mathrm{-6}y$
How many times higher could an astronaut jump on the Moon than on Earth if her takeoff speed is the same in both locations (gravitational acceleration on the Moon is about on-sixth of that on Earth)?
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