



 
Marioneta, By the form of the function $f(x) =  \frac{1}{80} x^2 + \frac12 x + 8$ the shape of the arc is a parabola opening downwards. When $x = 0$ m the height of the parabola is 8 m and when $x = 40$ m the height is again 8 m. You should check this. The vertex of the parabola is then midway between 0 m and 40 m. What is the height of the parabola there? If the boat has a tall mast like a sailing ship then, if it sails down the centre of the channel it can have a height that just fits under the vertex. If it is box shaped then the maximum height will depend on the width of the boat. Penny  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 