Question

A stone is dropped into a well and the report of the stone striking the bottom is heard $7.7$ seconds after it is dropped. Assume that the stone falls $16t^2$ feet in $t$ seconds and that the velocity of sound is $1120$ feet per second. The depth of the well is:

$784$ ft.

$342$ ft.

$1568$ ft.

$156.8$ ft.

None of these

Answer: A

Concepts:distance rate and time quadratic

Difficulty rating: 1670

Small Hint:

The total time is the falling time plus the sound’s return time

Big Hint:

If the falling time is $t$ , solve $t+\dfrac{16t^2}{1120}=7.7$

Solution:

If the stone falls for $t$ seconds, the depth is $16t^2,$ and the sound takes $\frac{16t^2}{1120}=\frac{t^2}{70}$ seconds to return. Hence $t+\frac{t^2}{70}=7.7,$ or $t^2+70t-539=0.$ The positive root is $t=7,$ giving depth $16(7^2)=784$ feet.

Thus, the correct answer is A.

1951 AMC 12 Problem 39

Answer: A

Difficulty rating: 1670

Small Hint:

Big Hint:

Solution:

Problem 39 in Other Years