In a tempering process, a glass plate that is initially at a uniform temperature ti is cooled by suddenly reducing the temperature of both surfaces to ts. the plate is 200 mm thick and the glass has a thermal diffusivity of 6 x 10-7 m2/s. how long will it take for the mid-plane temperature to achieve 50% of the maximum possible temperature reduction?

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.