Asquare piece of tin has 12 inches on a side. an open box is formed by cutting out equal square pieces at the corners and bending upward the projecting portion which remain. find the maximum volume that can be obtained.

Explanation:

Given a square Piece whose side is 12 inches

Now square pieces are cut from each corner to make it a open box

Suppose x is the length of square piece at each corner

then

base square has a length of

Dimension of new box is

Volume

For maximum volume differentiate with respect to x we get

we get x=6 and 4 but at x=6 volume becomes zero therefore x=4 is valid

its a 5.5 n

glad that

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft