Question

Even though Alice visits the wishing well frequently and always tosses in a coin for good luck, none of her wishes have come true. As a result, she decides to change her strategy and make a more emphatic statement by throwing the coin downward into the well. If the water is 8.23 m below the point of release and she hears the splash 0.93 seconds later, determine the initial speed at which she threw the coin. (Take the speed of sound to be 343 m/s.)

Answer 1

To determine the initial speed at which Alice threw the coin, we can use the equation of motion for a falling object. Using the given values, we can calculate the initial speed to be approximately 8.22 m/s.

Step-by-step explanation:

In this problem, we can use the equation of motion for a falling object to determine the initial speed at which Alice threw the coin. The equation is given by:

h = vi * t + (1/2) * g * t^2

Where h is the height of the water, vi is the initial speed of the coin, t is the time of flight, and g is the acceleration due to gravity.

From the problem, we know that the height of the water is 8.23 m, the time of flight is 0.93 s, and the speed of sound is 343 m/s. We can rearrange the equation to solve for vi:

vi = (h - (1/2) * g * t^2) / t

Substituting the known values, we have:

vi = (8.23 - (1/2) * 9.8 * 0.93^2) / 0.93

Simplifying, we get:

vi ~ 8.22 m/s

Answer 2

Answer: 4.29 m/s

Step-by-step explanation:

Given

Depth of the well, s = 8.23 m

Time taken to reach the well, t = 0.93 s

Speed of sound = 343 m/s

To solve this, we would be using one of l the laws of motion.

S = ut + 1/2gt², where

S = depth of the well

u = initial speed of toss

g = acceleration due to gravity

t = time taken to reach the well

We would then have

8.23 = 0.93 u + 1/2 * 9.8 * 0.93²

8.23 = 0.93 u + 4.9 * 0.8649

8.23 = 0.93 u + 4.23801

0.93 u = 8.23 - 4.23801

0.93 u = 3.99199

u = 3.99199 / 0.93

u = 4.29 m/s

Therefore, the initial speed of the coin is 4.29 m/s