For a given projectile, launched at an angle of 45 ° with the horizontal. Initial velocity is 64 feet per sec , find the parametric equations for the path of the projectile in terms of the parameter t representing time.
For a given projectile, launched at an angle of 45 ° with the horizontal. Initial velocity is 64 feet per sec , find the parametric equations for the path of the projectile in terms of the parameter t representing time.
Solution Summary: The author explains the parametric equations for the path of a projectile in terms of the parameter t representing time.
To calculate: For a given projectile, launched at an angle of 45° with the horizontal.
Initial velocity is 64 feet per sec, find the parametric equations for the path of the projectile in terms of the parameter t
representing time.
(b)
To determine
To calculate: The projectile is launched at an angle of 45° with the horizontal. The initial velocity is 64 feet per sec is given, find the angle α that the camera makes with the horizontal in terms of x and y and interms of t.
(c)
To determine
To calculate: The equation is α=tan−1(322t−16t2322t+50) is given, find the value of dαdt.
(d)
To determine
To graph: The provided equation is α=tan−1(322t−16t2322t+50), graph the provided equation of α in terms of t and find out if the graph is symmetric to the axis of parabolic arch of the projectile and also determine the time at which the rate of change of α is greatest.
(e)
To determine
To calculate: The provided equation is α=tan−1(322t−16t2322t+50), find the time at which the angle α is maximum and also find out if this occur when the projectile is at its greatest height.
The parametric equations of the function are given asx=asin²0, y = acos). Calculate
[Let: a=anumerical coefficient]
dy
d²y
and
dx
dx2
A tank contains 200 gal of fresh water. A solution containing 4 lb/gal of soluble
lawn fertilizer runs into the tank at the rate of 1 gal/min, and the mixture is
pumped out of the tank at the rate of 5 gal/min. Find the maximum amount of
fertilizer in the tank and the time required to reach the maximum.
Find the time required to reach the maximum amount of fertilizer in the tank.
t=
min
(Type an integer or decimal rounded to the nearest tenth as needed.)
Thumbi Irrigation Scheme in Mzimba district is under threat of flooding. In order to
mitigate against the problem, authorities have decided to construct a flood protection
bund (Dyke). Figure 1 is a cross section of a 300m long proposed dyke; together with its
foundation (key). Survey data for the proposed site of the dyke are presented in Table 1.
Table 2 provides swelling and shrinkage factors for the fill material that has been
proposed. The dyke dimensions that are given are for a compacted fill.
(1) Assume you are in the design office, use both the Simpson Rule and Trapezoidal
Rule to compute the total volume of earthworks required. (Assume both the dyke
and the key will use the same material).
(2) If you are a Contractor, how many days will it take to finish hauling the computed
earthworks using 3 tippers of 12m³ each? Make appropriate assumptions.
DIKE CROSS SECTION
OGL
KEY (FOUNDATION)
2m
1m
2m
8m
Figure 1: Cross section of Dyke and its foundation
1.5m from highest OGL
0.5m…
Chapter 13 Solutions
Student Solutions Manual For Larson/edwards? Multivariable Calculus, 11th
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