A pitcher throws a softball toward home plate. When the ball hits the catcher’s mitt, its horizontal velocity is 32 meters/second. The softball’s velocity goes to 0 meters/second in 0.8 seconds when caught. If the softball has a mass of 0.2 kilograms, what’s the force of the impact? Use F = ma, where .

Carbon is allowed to diffuse through a steel plate 15 mm thick. the concentrations of carbon at the two faces are 0.65 and 0.30 kg c/m^3 fe, which are maintained constant. if the preexponential and activation energy are 6.2 x 10-7 m2 /s and 80,000 j/mol, respectively, compute the temperature at which the diffusion flux is 1.43 x 10^-9 kg/m^2 -s.

You have a resistor and a capacitor of unknown values. first, you charge the capacitor and discharge it through the resistor. by monitoring the capacitor voltage on an oscilloscope, you see that the voltage decays to half its initial value in 2.70 miss . you then use the resistor and capacitor to make a low-pass filter. what is the crossover frequency fc?

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k