66. A boat travels at a speed 6.75 m/s in still water is to go directly across a river and back (Fig 3.31). The current flows 0.50 m/s (a) at what angle(s) must the boat be steered (b) How long does it take to make the roundtrip? (Assume that the boat's is constant at all times, and neglect turn around time.)
88. An astronaut on the moon fires a projectile from a launcher on a level surface so as to get the maximum range if the launcher gives the projectile a muzzle velocity 25 m/s, what is the range of the projectile [Hint: the acceleration due to gravity on the moon is only one six of that on earth.]
(I should mention that I know the angle of incline of the gun is at 45 degrees, since this provides the maximum range no matter what the g value is. I also know that since . Also, y = 0 m since the projectile is being fired over a planar surface, so the projectile hits the ground at the same height it left at. g is, of course, equal to 1/6 times 9.8 m/s^2 in this case.)
Now, we want the range x. So
We don't know t.
So look at the y information. We know that
Solve this for t and plug it into the x equation to get the range.