The telescopes on some commercial surveillance satellites can resolve objects on the ground as small as 85 cm across (see Google Earth), and the telescopes on military surveillance satellites reportedly can resolve objects as small as 10 cm across. Assume first that object resolution is determined entirely by Rayleigh’s criterion and is not degraded by turbulence in the atmosphere. Also assume that the satellites are at a typical altitude of 400 km and that the wavelength of visible light is 550 nm. What would be the required diameter of the telescope aperture for (a) 85 cm resolution and (b) 10 cm resolution? (c) Now, considering that turbulence is certain to degrade resolution and that the aperture diameter of the Hubble Space Telescope is 2.4 m, what can you say about the answer to (b) and about how the military surveillance resolutions are accomplished?
The telescopes on some commercial surveillance satellites can resolve objects on the ground as small as 85 cm across (see Google Earth), and the telescopes on military surveillance satellites reportedly can resolve objects as small as 10 cm across. Assume first that object resolution is determined entirely by Rayleigh’s criterion and is not degraded by turbulence in the atmosphere. Also assume that the satellites are at a typical altitude of 400 km and that the wavelength of visible light is 550 nm. What would be the required diameter of the telescope aperture for (a) 85 cm resolution and (b) 10 cm resolution? (c) Now, considering that turbulence is certain to degrade resolution and that the aperture diameter of the Hubble Space Telescope is 2.4 m, what can you say about the answer to (b) and about how the military surveillance resolutions are accomplished?
The telescopes on some commercial surveillance satellites can resolve objects on the ground as small as 85 cm across (see Google Earth), and the telescopes on military surveillance satellites reportedly can resolve objects as small as 10 cm across. Assume first that object resolution is determined entirely by Rayleigh’s criterion and is not degraded by turbulence in the atmosphere. Also assume that the satellites are at a typical altitude of 400 km and that the wavelength of visible light is 550 nm. What would be the required diameter of the telescope aperture for (a) 85 cm resolution and (b) 10 cm resolution? (c) Now, considering that turbulence is certain to degrade resolution and that the aperture diameter of the Hubble Space Telescope is 2.4 m, what can you say about the answer to (b) and about how the military surveillance resolutions are accomplished?
A skateboarder with his board can be modeled as a particle of mass 80.0 kg, located at his center of mass. As shown in the figure below, the skateboarder starts from rest in a crouching position at one lip of a half-pipe (point). On his descent, the skateboarder moves without friction so
that his center of mass moves through one quarter of a circle of radius 6.20 m.
i
(a) Find his speed at the bottom of the half-pipe (point Ⓡ).
m/s
(b) Immediately after passing point Ⓑ, he stands up and raises his arms, lifting his center of mass and essentially "pumping" energy into the system. Next, the skateboarder glides upward with his center of mass moving in a quarter circle of radius 5.71 m, reaching point D. As he
passes through point ①, the speed of the skateboarder is 5.37 m/s. How much chemical potential energy in the body of the skateboarder was converted to mechanical energy when he stood up at point Ⓑ?
]
(c) How high above point ① does he rise?
m
A 31.0-kg child on a 3.00-m-long swing is released from rest when the ropes of the swing make an angle of 29.0° with the vertical.
(a) Neglecting friction, find the child's speed at the lowest position.
m/s
(b) If the actual speed of the child at the lowest position is 2.40 m/s, what is the mechanical energy lost due to friction?
]
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