Abead of mass m under the influence of gravity slides along a frictionless and massless wire whose height is given by a function y(x). assume that at position (x, y) = (0, 0) the tangent of the wire is horizontal and the bead passes this point with a given speed v0. what should y(x) be so that the horizontal speed remains v0 at all times (that is what is the shape of the wire)? one simple solution is y = 0, find the other solution. (hint: it should

y = constant

Explanation:

Bodies moving on the surface of Earth are subject to gravity, and they have a potential and kinetic energy. If there is no friction, the sum of the kinetic and potential energy remains constant.

Since potential energy depends on height, changes in altitude affect potential energy. Going higher increases this energy, this is accompanied by a reduction of kinetic energy and speed (since kinetic energy is related to speed). If the body goes down potential energy is reduced, but kinetic energy and speed increase.

For speed to remain constant the kinetic energy must remain constant. For the kinetic energy to remanin constant, the potential energy must remain constant, and for the potential energy to remain constant the height must remain constant.

he kicked it 10 feet straight up into the air? i think this works.

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft