Page 297 - Calculus Demystified

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Fig. S3.9 Solutions to Exercises

11. The acceleration due to gravity, near the surface of the earth, is about
2
−32 ft/sec regardless of the mass of the object being dropped. The two
stones will strike the ground at the same time.
12. He can drop a rock into the well and time how long it takes the rock to strike
the water. Then he can use the equation
2
p(t) =−16t + 0t + h 0
to solve for the depth. If the well is very deep, then he will have to know
the speed of sound and compensate for how long it takes the splash to reach
his ears.
13. Refer to Fig. S3.13 to see the geometry of the situation.
Let (x, y) be the point where the rectangle touches the line. Then the area
of the rectangle is
A = x · y.

But of course 3x + 5y = 15 or y = 3 − (3/5)x. Hence
A = x ·[3 − (3/5)x].
We may differentiate and set equal to zero to find that x = 5/2 and y = 3/2
is the solution to our problem.
14. Let s be a side of the base and let h be the height. The area of the base is s 2
and the same for the top. The area of each side is s · h. Thus the cost of the
base and top is
2
2
C 1 =[s + s ]· 10 cents