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 be a familiar shape that might make sense in hindsight). note that energy is conserved.

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

3. dark matter

empty space could also be a simple vacuum

96.77 amp

explanation:

rl = 250/100 = 2.5 ohms.

egl = 250 + (100 × 0.1) + 2 = 262 v.

at 700 r.p.m., eg2 = 262 × 700/1000 = 183.4 v.

if ia is the new current, then eg2 - 2 - (ia × 0.1) = 2.5 ia

which means this will give ia = 96.77 amp.