Explanation:
We know that the sky appears to us like a sphere called as celestial sphere which appears to rotate around an imaginary axis because of Earth's rotation. Since the axis cuts the celestial sphere at celestial poles all the object seems to circle around the celestial poles.
Condition 1: The stars rise and set perpendicular to the horizon
The observer is at the equator
Condition 2: The stars circle the sky parallel to the horizon
The observer is at the Pole of the Earth
Condition 3: The celestial equator passes through the zenith
The observer is at the equator
Condition 4: In the course of a year, all stars are visible
The observer is at the equator
Condition 5: The Sun rises on March 21 and does not set until September 21 (ideally)
The observer is at North Pole
Before the engines fail
, the rocket's horizontal and vertical position in the air are


and its velocity vector has components


After
, its position is


and the rocket's velocity vector has horizontal and vertical components


After the engine failure
, the rocket is in freefall and its position is given by


and its velocity vector's components are


where we take
.
a. The maximum altitude occurs at the point during which
:

At this point, the rocket has an altitude of

b. The rocket will eventually fall to the ground at some point after its engines fail. We solve
for
, then add 3 seconds to this time:

So the rocket stays in the air for a total of
.
c. After the engine failure, the rocket traveled for about 34.6 seconds, so we evalute
for this time
:

V = IR
I = V/R
I = 12/6
I = 2 amps
Question:
A particle moving along the x-axis has a position given by x=(24t - 2.0t³)m, where t is measured in s. What is the magnitude of the acceleration of the particle at the instant when its velocity is zero
Answer:
24 m/s
Explanation:
Given:
x=(24t - 2.0t³)m
First find velocity function v(t):
v(t) = ẋ(t) = 24 - 2*3t²
v(t) = ẋ(t) = 24 - 6t²
Find the acceleration function a(t):
a(t) = Ẍ(t) = V(t) = -6*2t
a(t) = Ẍ(t) = V(t) = -12t
At acceleration = 0, take time as T in velocity function.
0 =v(T) = 24 - 6T²
Solve for T
Substitute -2 for t in acceleration function:
a(t) = a(T) = a(-2) = -12(-2) = 24 m/s
Acceleration = 24m/s
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<em><u>hope it helps you</u></em>
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