[7 pts] 1. Suppose that a car starts from rest, its engine providing an acceleration of 4 ft/s2 while air resistance provides 0.
1 ft/s2 of deceleration for each ft per s (foot per second) of the car’s velocity. Set up an Initial Value Problem (IVP) for the velocity of the car. Solve the IVP and use the solution to find the car’s limiting velocity. If the car starts at position x(0) = x0 = 0, ft, what position will it be at after 1 2 hour? Be sure to set up your coordinate system and include units in all of your answers.
1 answer:
Answer:
a) Initial Value Problem
dv/dt = 4 - 0.1v
v(0) = 0
b) solution to the IVP
v(t) = 40(1 - e^(-t/10))
c) Limiting velocity
Vo = 40 ft/s
Position of the car after 12 hours
X = 14,390 ft
Explanations:
The complete explanations of each of the sections contained in the question are in the files attached to this solution.
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<h2>Answer: 277.777 m</h2>
Explanation:
The situation described here is parabolic movement. However, as we are told that the rock was<u> projected upward from the surface</u>, we will only use the equations related to the Y axis.
In this sense, the movement equations in the Y axis are:
(1)
(2)
Where:
is the rock's final position
is the rock's initial position
is the rock's initial velocity
is the final velocity
is the time the parabolic movement lasts
is the acceleration due to gravity at the surface of the moon
As we know , equation (2) is rewritten as:
(3)
On the other hand, the maximum height is accomplished when :
(4)
(5)
Finding :
(6)
Substituting (6) in (3):
(7)
(8) Now we can calculate the maximum height of the rock
(9)
Finally: