In an annealing process, a 50-mm-thick stainless steel plate (rho = 8238 kg/m3, cp = 468 j/kg·k, k = 13.4 w/m·k, and α = 3.48 × 10−6 m2/s ) was reheated in a furnace from an initial uniform temperature of 230°c. the ambient temperature inside the furnace is uniform at 1000°c, and the convection heat transfer coefficient is 215 w/m2·k. if the entire stainless steel plate is to be heated to at least 600°c, determine the time that the plate should be heated in the furnace using the analytical one-term approximation method.

Aball is thrown from the top of a building with an initial velocity of 21.9 m/s straight upward, at an initial height of 51.6 m above the ground. the ball just misses the edge of the roof on its way down, as shown in the figure. (a) determine the time needed for the ball to reach its maximum height. (b) determine the maximum height. (c) determine the time needed for the ball to return to the height from which it was thrown, and the velocity of the ball at that instant. (d) determine the time needed for the ball to reach the ground. (e) determine the velocity and position of the ball at t = 5.35 s.