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Old Sep 14th 2018, 09:32 AM   #1
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Hi, will u help me guys? :)

A special vehicle moves at a speed v on a flat frozen surface
Lakes. Maximum force tangent to the surface of the lake, with which the vehicle can operate on this surface,
it has an F value and does not depend on its velocity or the angle between the vector of this force
and the vehicle speed vector. The vehicle does not have a system recovering energy when braking.
How does this vehicle move if it changes speed to speed perpendicular to speed
initial, but with the same value
a) in such a way that the speed change lasts as short as possible?
b) in such a way that the work done could be the smallest?
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Old Sep 15th 2018, 04:14 AM   #2
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What does "changes speed to speed perpendicular to speed
initial" mean?
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Old Sep 16th 2018, 08:32 AM   #3
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I think what he means is the vehicle makes a turn such that its new velocity vector is perpendicular to the original velocity vector, and with with same magnitude. In other words the vehicle turns right (or left) 90 degrees.

To the OP: there are a couple of ways the vehicle could do this. It could move in a continuous arc of radius R using the tangential force F such that F = mv^2/R, maintaining constant magnitude of velocity. Or it could slow down a bit, perhaps even to zero, enabling it to make a sharper turn, then speed up again. So ask yourself how much work is done in these two different scenarios, and which is quicker to execute?
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