Starting at t =0 and x =0, a boat of mass m is gliding with initial velocity v₀ in water and is slowed down by a retarding force of magnitude cv², where c is a constant.

3) Starting at t = and I = I}, a boat of mass m is gliding with initial velocity on in water and is slowed down by a retarding force of magnitude cog, Where c is a constant. a) Specify the dimensions of the given constants, and combine them to form natural units of length, L0, and time, To (use no as a unit ofvelocity)- 1)) Write a differential equation representing the situation and nondimensionalize it (write it in terms of dimensionless quantities like 6 E also and t E 1'] Th). e} Integrate to nd 5(3). Pay careful attention to the limitsfinitial conditions (i e. what is 5.3). d) integrate to nd r\"), Where 5: : gem. and g 2 5(5)- e) How much time does it take for the velocity,r n to fall to half its initial value, and how far (in x) has the boat travelled during that time