A model rocket is fired horn the roof of a 50 ft tall building as shown in Fig. P8.1.
The height of the rocket is given by
where
(a) Write the
(b) The velocity
(c) The acceleration
(d) The time required to reach the maximum height as well as the corresponding height
(a)
The quadratic equation for the height of the rocket.
Answer to Problem 1P
The quadratic equation for the height is
Explanation of Solution
Given:
The height of the rocket is
.......(1)
The initial height of the rocket is
The initial velocity of the rocket is
The value of acceleration due to gravity is
Calculation:
Substitute for for and for in equation (1).
Conclusion:
Thus, the quadratic equation for the height is
(b)
The velocity
Answer to Problem 1P
The velocity is
Explanation of Solution
Concept used:
Write the expression for the velocity
.......(2)
Here, is the velocity and is the height of the rocket at time
Calculation:
Substitute for in equation (2).
Conclusion:
Thus, the velocity is
(c)
The acceleration
Answer to Problem 1P
The acceleration is
Explanation of Solution
Concept used:
Write the expression for the acceleration.
.......(3)
Here, the is the acceleration and is the velocity of the rocket at time
Calculation:
Substitute for in equation (3).
Conclusion:
Thus, the acceleration is
(d)
The time required to reach the maximum height, as well as, corresponding maximum height and sketch the result and use the result to sketch
Answer to Problem 1P
The maximum height of the rocket is at and sketch for the height
is drawn as shown in Figure 1.
Explanation of Solution
Concept used:
Write the expression for the maximum height.
.......(4)
Calculation:
Equate the derivative of to zero
Substitute for in equation (4).
Rearrange for
Therefore, the time at maximum height is
Write the expression for maximum height of the rocket.
.......(5)
Substitute for in equation (5).
Therefore, the maximum height of the rocket reached is
The sketch for the height is drawn as shown in Figure 1.
Conclusion:
Thus, the maximum height of the rocket is at and sketch for the height
is drawn as shown in Figure 1.
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- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage