Concept explainers
Students are testing their new drone to see if it can safely deliver packages to different departments on campus. Position data can be approximated using the expressions
(a)
The duration of flight.
Answer to Problem 11.182RP
We got the time of flight is
Explanation of Solution
Given information:
Time
Concept used:
We shall draw graph (plot of path)
Calculation:
Following table is made-
t | 0.00 | 1.00 | 10.00 | 20.00 | 30.00 | 39.00 | 40.00 | 50.00 | 60.00 | 70.00 |
x(t) | 0.00 | 0.01 | 3.78 | 24.40 | 71.78 | 141.11 | 150.40 | 259.38 | 392.40 | 537.78 |
y(t) | 0.00 | 0.93 | 87.89 | 300.06 | 512.20 | 599.08 | 600.00 | 512.02 | 299.82 | 87.72 |
t | 79.00 | 80.00 | 81.00 | 82.00 |
x(t) | 665.15 | 678.40 | 691.38 | 704.07 |
y(t) | 0.91 | 0.00 | 0.94 | 3.73 |
Plot,
From above table and plot we get the take off and landing altitudes are the same at
Hence the time of flight is
Conclusion:
We got the time of flight is
(b)
The maximum speed in x direction.
Answer to Problem 11.182RP
We got the maximum horizontal speed
Explanation of Solution
Given information:
Time
Concept used:
Speed
For maximum speed
Calculation:
Speed
For maximum speed
On putting value of
Conclusion:
We got the maximum horizontal speed
(c)
The maximum altitude
The horizontal distance of the flight.
Answer to Problem 11.182RP
We get the maximum altitude,
And horizontal distance traveled,
Explanation of Solution
Given information:
Time
Concept used:
We shall draw graph (plot of path)
Calculation:
Following table is made-
t | 0.00 | 1.00 | 10.00 | 20.00 | 30.00 | 39.00 | 40.00 | 50.00 | 60.00 |
x(t) | 0.00 | 0.01 | 3.78 | 24.40 | 71.78 | 141.11 | 150.40 | 259.38 | 392.40 |
y(t) | 0.00 | 0.93 | 87.89 | 300.06 | 512.20 | 599.08 | 600.00 | 512.02 | 299.82 |
t | 70.00 | 79.00 | 80.00 | 81.00 | 82.00 |
x(t) | 537.78 | 665.15 | 678.40 | 691.38 | 704.07 |
y(t) | 87.72 | 0.91 | 0.00 | 0.94 | 3.73 |
Plot,
From above table and plot we get the maximum altitude,
And horizontal distance travelled,
Conclusion:
We get the maximum altitude,
And horizontal distance travelled,
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Chapter 11 Solutions
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