Question

The distance to the surface of the water in a well can sometimes be found by dropping an object into the well and measuring the time elapsed until a sound is heard. If t is the time (in seconds) it takes for the object to strike the water, then ty obeys the equation s 16t, where s is the distance (in feet) Solving for ty, we have t/4. Let t2 be the time it takes for the sound of the impact to reach your ears. Since sound waves travel at a speed of approximately 1100 feet per second, the time to travel the distance s is t2 s/1100. Now t1 +t2 is the total time that elapses from the moment that the object is dropped to the moment that a sound is heard. We have the equation Vs Total elapsed time t1 + 100 Fi

Answer 1

THE QUESTION IS NOT PROPERLY WRITTEN

The distance to the surface of the water in a well can sometimes be found by dropping an object into the well and measuring the time elapsed until a sound is heard. If t1 is the time (in seconds) it takes for the object to strike the water, then t1 obeys the equation s = 16t1², where s is the distance (in feet) Solving for t1, we have t1 = √s/4. Let t2 be the time it takes for the sound of the impact to reach your ears. Since sound waves travel at a speed of approximately 1100 feet per second, the time to travel the distance s is t2 = s/1100. Now t1 +t2 is the total time that elapses from the moment that the object is dropped to the moment that a sound is heard. We have the equation; Total elapsed time √s/4 + s/1100.

Find the distance to the water’s surface if the total time elapsed from dropping a rock to hearing it hit water is 4 seconds.

Answer:

229.94 feet

Step-by-step explanation:

Given

t1 = √s/4

t2 = s/1100

From the question, we understand that

t1 + t2 = 4 seconds

Let y = √s

So,

t1 + t2 = 4 becomes

√s/4 + s/1100 = 4

y/4 + y²/1100 = 4 ------ Solve the fractions

(275y + y²)/1100 = 4

275y + y² = 4 * 1100

275y + y² = 4400 ------- Rearrange

y² + 275y - 4400 = 0 (Quadratic Equation)

The standard form of a quadratic equation is ax² + bx + c = 0

Where x =

frac{-b+-\sqrt{bx^{2} - 4ac } }{2a}

Here a = 1, b = 275 and c = -4400

So,

y = (-275+- √(275² - 4*1*-4400))/2

y = (-275+- √75625 + 17600))/2

y = (-275+- √(93225))/2

y = (-275 +- 305.328)/2

y = (-275 + 305.328)/2 or (-275-305.328)/2

y = 30.328/2 or -580.328/2

y = 15.164 or -290.164 -------Negative is not applicable

So, y = 15.164

But y = √s

So, s = y²

S = 15.164²

s = 229.94 ft