F-1 (8.5 Points): Hypothetically, a hail drops straight down to the ground. At a reasonable height measured from the ground, the hail's initial speed is 120 and initial mass is m0. Its later mass, depending on its speed 12 due to . . . m T? . . . melting or absorptlon, lS expressed as m: 0 and its a1r reSIStance 1.7 is kv where k is a constant. The earth's gravitational constant is 9. Some assumptions were made here to ease your math at the price of the physics rigor. Please (1) establish the [VP for the motion of the hail (3.0 pts); and (2) calculate the hail's speed at drop height yin terms of m0, 120, k, g. (5.5 pts) F-2: Use any method(s) to find the GS's of 2 unrelated DE's: (4.5 pts for (1) and 4.0 pts for (2)) (1) 2y' ty2 - 3x -2 = 0 (2) xy' - y - y' cosx = 0 All needed info is given so please do not ask for more.F-3: Use LT (4.5 pts) and one other method (4.0 pts) to find the PS of x =y+z+1 y' =z+x+1 z' =xty+1 with ICs x(0) = y(0) = z(0) = 0. Convolutions, if any, must be evaluated.F-4: Use LT (4.5 pts) and one non-LT (4.0 pts) method to find the PS of (y"" +y"+y'ty = sin x + cosx y"(0) = y'(0) = y(0) = 0 Your solution may not contain convolution (). Thus, convolutions, if any, must be evaluated