The Hubble Space Telescope was launched into space in 1990 and now orbits the Earth at 5 mi/sec at a distance of 353 mi above the Earth. From its location in space, the Hubble is free from the distortion of the Earth’s atmosphere, enabling it to return magnificent images from distant stars and galaxies. The quality of the Hubble’s images result from a large parabolic mirror, 2.4 m (7.9 ft) in diameter, that collects light from space. Suppose that a coordinate system is chosen so that the vertex of a cross section through the center of the mirror is located at ( 0 , 0 ) . Furthermore, the focal length is 57.6 m. a. Assume that x and y are measured in meters. Write an equation of the parabolic cross section of the mirror for − 1.2 ≤ x ≤ 1.2 . See figure. b. How thick is the mirror at the edge? That is, what is the y value for x = 1.2 ?
The Hubble Space Telescope was launched into space in 1990 and now orbits the Earth at 5 mi/sec at a distance of 353 mi above the Earth. From its location in space, the Hubble is free from the distortion of the Earth’s atmosphere, enabling it to return magnificent images from distant stars and galaxies. The quality of the Hubble’s images result from a large parabolic mirror, 2.4 m (7.9 ft) in diameter, that collects light from space. Suppose that a coordinate system is chosen so that the vertex of a cross section through the center of the mirror is located at ( 0 , 0 ) . Furthermore, the focal length is 57.6 m. a. Assume that x and y are measured in meters. Write an equation of the parabolic cross section of the mirror for − 1.2 ≤ x ≤ 1.2 . See figure. b. How thick is the mirror at the edge? That is, what is the y value for x = 1.2 ?
Solution Summary: The author calculates the parabolic cross section of the mirror for 2.4m that collects light form space.
The Hubble Space Telescope was launched into space in 1990 and now orbits the Earth at 5 mi/sec at a distance of 353 mi above the Earth. From its location in space, the Hubble is free from the distortion of the Earth’s atmosphere, enabling it to return magnificent images from distant stars and galaxies. The quality of the Hubble’s images result from a large parabolic mirror, 2.4 m (7.9 ft) in diameter, that collects light from space.
Suppose that a coordinate system is chosen so that the vertex of a cross section through the center of the mirror is located at
(
0
,
0
)
. Furthermore, the focal length is 57.6 m.
a. Assume that x and y are measured in meters. Write an equation of the parabolic cross section of the mirror for
−
1.2
≤
x
≤
1.2
. See figure.
b. How thick is the mirror at the edge? That is, what is the y value for
x
=
1.2
?
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.
The figure shows a device that can be used to measure the speed of a bullet. The device consists of two rotating disks, separated by a distance of d = 0.808 m, and rotating with an angular speed of 99.2 rad/s. The bullet first passes through the left disk and then through the right disk. It is found that the angular displacement between the two bullet holes is = 0.237 rad. From these data, determine the speed of the bullet.
Consider a tall building located on the Earth's equator. As the Earth rotates, a person on the top floor of the building moves faster than someone on the ground with respect to
an inertial reference frame because the person on the ground is closer to the Earth's axis. Consequently, if an object is dropped from the top floor to the ground a distance h
below, it lands east of the point vertically below where it was dropped.
(a) How far to the east will the object land? Express your answer in terms of h, g, and the angular speed w of the Earth. Ignore air resistance and assume the free-fall
acceleration is constant over this range of heights.
Ax =
(b) Evaluate the eastward displacement (in cm) for h = 52.0 m.
cm
(c) In your judgment, were we justified in ignoring this aspect of the Coriolis effect in our previous study of free fall?
O Yes
No
(d) Suppose the angular speed of the Earth were to decrease with constant angular acceleration due to tidal friction. Would the eastward displacement…
A
A jet airliner is flying at a constant altitude of 10,000 m above sea level as it
approaches a Pacific island. The aircraft comes within the direct line of sight of a
radar station located on the island, and the
radar indicates the initial angle between sea
level and its line of sight to the aircraft is 30°.
How fast (in kilometers per hour) is the
aircraft approaching the island when first
detected by the radar instrument if it is
turning upward (counterclockwise) at the
1 deg
rate of in order to keep the aircraft
3 s
within its direct line of sight?
R
0
10,000
X
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY