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Sketch the indicated curves by the methods of this section. You may check the graphs by using a calculator.The altitude $h$ (in $\mathrm{ft}$ ) of a certain rocket is given by $h=-t^{3}+54 t^{2}+480 t+20,$ where $t$ is the time (in s) of flight. Sketch the graph of $h=f(t)$

Calculus 1 / AB

Chapter 24

Applications of the Derivative

Section 5

Using Derivatives in Curve Sketching

Derivatives

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Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

02:47

Ignore air resistance.Sket…

00:48

Use your CAS or graphing c…

04:48

Launching a rocket A small…

07:43

A small rocket is launched…

01:03

00:52

08:49

The motion of a jet plane …

10:05

A rocket is fired upward f…

03:37

A model rocket is launched…

04:38

The formula for the height…

we have a baseball pitcher throwing a ball from a height of six feet toward a plate to 60 feet away, and he's gonna release the ball with a speed of 130 feet per second. We want to determine the height of the ball as it crosses the flip as a crosses the plate. The vertical position formula is going to be negative 16 t square plus visa bough T. But the original vertical velocity is zero, so we don't need to worry about that middle term and then plus y Sebo, which is the initial height, which would be six feet. The horizontal position function x of T off would eat well. 130 the horizontal velocity times the time it's traveling now, in order to figure out the height of it as a crosses the plate, we're gonna have to figure how long it takes this ball to travel 60 horizontal meters. Now, on your calculator. If you were to graph those Parametric equations, you get a graph that looks something like this. It's half of a parabola. Start to the height of six, and when it's 60 feet away, you're gonna see that its above the ground. Okay, first for the time that it takes to travel 60 meters, we're just going to go to the horizontal motion formula. I'm gonna fill in 64 x empty. Since that the distance that we wanted to travel, I will divide 60 by 130 which wouldn't give me point 462 So it takes 0.462 seconds to reach the plate. So now let's figure the height of it. At that point, I will fill in 0.462 seconds for the time. So I have negative 16 times 160.462 squared, plus six fourth vertical position. And when we feel that in, we get a high of 2.5 eight feet. So the pitches up 2.58 feet above the plate when it crosses

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In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

Ignore air resistance.Sketch the parametric graphs as in example5.4 to i…

Use your CAS or graphing calculator to sketch the plane curves defined by th…

Launching a rocket A small rocket is launched vertically upward from the edg…

A small rocket is launched vertically upward from the edge of a cliff $80 \m…

The motion of a jet plane just after landing on a runway is described by the…

A rocket is fired upward from the ground with an initial velocity of 100 fee…

A model rocket is launched straight upward. Its altitude $y$ as a function o…

The formula for the height of a projectile is$$s(t)=-16 t^{2}+v_{0} t+s_…

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