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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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