Concept explainers
(a)
The maximum height gain by the space vehicle.
(a)
Answer to Problem 32AP
The maximum height gain by the space vehicle is
Explanation of Solution
Given info: The initial speed of the vehicle is
Formula to calculate the maximum height gain by the space vehicle by the conservation of energy is,
Here,
Formula to calculate the kinetic energy of the space vehicle at the Earth’s surface is,
Here,
Formula to calculate the potential energy of the space vehicle at the Earth’s surface is,
Here,
The mass of the Earth is
The value of universal gravitational constant is
Formula to calculate the potential energy space vehicle at the altitude is,
Here,
The final kinetic energy of the space vehicle is zero because the space vehicle is rest at that point.
Substitute
Further solve the above expression.
Write the expression for the acceleration due to gravity.
Here,
Substitute
Conclusion:
Therefore, the maximum height gain by the space vehicle is
(b)
The speed of the meteorite to strike the Earth.
(b)
Answer to Problem 32AP
The speed of the meteorite to strike the Earth is
Explanation of Solution
Given info: The initial speed of the vehicle is
From equation (2), the expression for the speed is given as,
Here,
Further solve the above expression.
Substitute
Conclusion:
Therefore, the speed of the meteorite to strike the Earth is
(c)
To show: The result from part (a) is consistent with
(c)
Answer to Problem 32AP
The result from part (a) is consistent with
Explanation of Solution
Given info: The initial speed of the vehicle is
Consider a baseball is tossed up with an initial speed that is very small as compared to the escape speed.
Here,
As the initial speed that is very small. So the initial speed of the vehicle tends to be zero.
From part (a), the maximum height gain by the space vehicle is,
Substitute
Write the expression for the maximum height of the projectile motion of the baseball.
Here,
From maximum height of the projectile motion of the baseball, the value of angle of the projectile motion of the baseball should be
Substitute
From equations (3) and (4).
So, the maximum height gain by the space vehicle is consistent with
Conclusion:
Therefore, the result from part (a) is consistent with
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Chapter 13 Solutions
Physics for Scientists and Engineers with Modern Physics
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