a. The power necessary to maintain the speed of 15ms^-1 can be found using the equation for power, P = Force * velocity, where P is in watts, force is in newtons and velocity is in meters per second. Substituting the values given in the question, we get:
P = (400 + k * 15²) * 15
P = (400 + 11250) * 15
P = 11650 Watts
Therefore, the power necessary to maintain the speed of 15ms^-1 is approximately 11650 Watts.
b. The total resistive force at a speed of 30ms^-1 can be found by substituting 30 for v in the force equation:
F = 400 + k * 30^2
F = 12000 N
Therefore, the total resistive force at a speed of 30ms^-1 is approximately 12000 N.
c. The power required to maintain the speed of 30ms^-1 can be found using the same equation as in part a:
P = (400 + k * 30^2) * 30
P = (1500 + 600000) * 30
P = 625000000 Watts
Therefore, the power required to maintain the speed of 30ms^-1 is approximately 625000000 Watts. This is a very large amount of power and would require a significant amount of energy to maintain.