Lunar projectile motion A rock thrown vertically upward from the surface of the moon at a velocity of 24 $\mathrm{m} / \mathrm{sec}$ (about 86 $\mathrm{km} / \mathrm{h}$ ) reaches a height of $s=24 t-0.8 t^{2}$ meters in $t$ sec. a. Find the rock's velocity and acceleration at time $t .$ (The acceleration in this case is the acceleration of gravity on the moon.) b. How long does it take the rock to reach its highest point? c. How high does the rock go? d. How long does it take the rock to reach half its maximum height? e. How long is the rock aloft?
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$$s=24t-0.8t^2$$ $$\frac{ds}{dt}=24-1.6t$$ Show more…
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Lunar Projectile Motion A rock thrown vertically upward from the surface of the moon at a velocity of 24 $\mathrm{m} / \mathrm{sec}$ (about 86 $\mathrm{km} / \mathrm{h} )$ reaches a height of $s=24 t-0.8 t^{2}$ meters in $t$ seconds. (a) Find the rock's velocity and acceleration as functions of time. (The acceleration in this case is the acceleration of gravity on the moon.) (b) How long did it take the rock to reach its highest point? (c) How high did the rock go? (d) When did the rock reach half its maximum height? (e) How long was the rock aloft?
Derivatives
Velocity and Other Rates of Change
Lunar projectile motion A rock thrown vertically upward from the surface of the moon at a velocity of 24 $\mathrm{m} / \mathrm{sec}$ (about 86 $\mathrm{km} / \mathrm{h} )$ reaches a height of $s=24 t-0.8 t^{2} \mathrm{m}$ in $t \mathrm{sec}$ . a. Find the rock's velocity and acceleration at time $t$ . The accel- eration in this case is the acceleration of gravity on the moon.) b. How long does it take the rock to reach its highest point? c. How high does the rock go? d. How long does it take the rock to reach half its maximum height? e. How long is the rock aloft?
The Derivative as a Rate of Change
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