An airplane is flying at a constant height of 3000 ft above water at a speed of 400 ft/s . The pilot is to release a survival package so that it lands in the water at a sighted point P . If air resistance is neglected, then the package will follow a parabolic trajectory whose equation relative to the coordinate system in the accompanying figure is y = 3000 − g 2 υ 2 x 2 where g is the acceleration due to gravity and υ is the speed of the airplane. Using g = 32 ft/s 2 , find the “line of sightâ€� angle θ , to the nearest degree, that will result in the package hitting the target point.
An airplane is flying at a constant height of 3000 ft above water at a speed of 400 ft/s . The pilot is to release a survival package so that it lands in the water at a sighted point P . If air resistance is neglected, then the package will follow a parabolic trajectory whose equation relative to the coordinate system in the accompanying figure is y = 3000 − g 2 υ 2 x 2 where g is the acceleration due to gravity and υ is the speed of the airplane. Using g = 32 ft/s 2 , find the “line of sightâ€� angle θ , to the nearest degree, that will result in the package hitting the target point.
An airplane is flying at a constant height of
3000
ft
above water at a speed of
400
ft/s
. The pilot is to release a survival package so that it lands in the water at a sighted point
P
.If air resistance is neglected, then the package will follow a parabolic trajectory whose equation relative to the coordinate system in the accompanying figure is
y
=
3000
−
g
2
υ
2
x
2
where
g
is the acceleration due to gravity and
υ
is the speed of the airplane. Using
g
=
32
ft/s
2
,
find the “line of sight� angle
θ
,
to the nearest degree, that will result in the package hitting the target point.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
To test the power of a car, a Dyno Test sets the wheels on rollers that are lifted off the
ground.
During one test on the car, a point on the tire has a minimum height of 30 cm, a
maximum height of 110 cm, and is spinning constantly at 5 rotations per 1 second.
A point on the tire can be model by the equation h =acos b(t-c) +d
where h represents the height of the point, in cm, and t represents time, in seconds.
If the point starts at the minimum, then the partial graph below shows a sinusoidal
function that could model the height of the point at different times in the rotation.
150
height
(cm)
100
+50
time (s)
5.
Determine a sinusoidal function of the form h=acos b(t-c) +d, that could
represent this situation.
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