Merry-go-round at an amusement park is initially at rest. It begins to rotate at time t = 0 . The angle through which it rotates is defined by θ(t) = ( t + ke−t/k) , where k is a positive constant, t is in seconds, and θ is in radians. Find the angular velocity of the merry-go-round at t = T.

Ajogger accelerates from rest to 4.86 m/s in 2.43 s. a car accelerates from 20.6 to 32.7 m/s also in 2.43 s. (a) find the magnitude of the acceleration of the jogger. (b) determine the magnitude of the acceleration of the car. (c) how much further does the car travel than the jogger during the 2.43 s?

Acricket ball of 70g moving with a velocity of 0.5 m/s is stopped by a player in 0.5s what is the force applied to stop the ball

Suppose that an electromagnetic wave which is linearly polarized along the x−axis is propagating in vacuum along the z−axis. the wave is incident on a conductor which is placed at z > 0 region of the space. the conductor has conductivity σ, magnetic permeability µ and electric permittivity ε. (a) find the characteristic time for the free charge density which dissipates at the conductor. (b) write the maxwell equations and derive the wave equation for a plane wave propagating in a conductor. (c) find the attenuation distance at which the incident amplitude reduces to e ^−1 of its initial value. (d) find the electric and magnetic fields inside the conductor. 8 (e) find the power loss per area of the incident electromagnetic wave at the surface of conductor.