A log is floating on swiftly moving water. A stone is dropped from rest from a 84-m-high bridge and lands on the log as it passes under the bridge. If the log moves with a constant speed of 3.6 m/s, what is the horizontal distance between the log and the bridge when the stone is released?

Will someone please help me step by step on how to do this confusing problem?

Find time is takes the stone to fall the 84m ( -84 = 1/2(-9.8)T^2 ). Then plug into Time x Velocity of log (3.6) = answer

Certainly! I'll walk you through the steps to solve this problem.

Step 1: Understand the problem
We're given the height of the bridge, the velocity of the log, and we need to find the horizontal distance between the log and the bridge when the stone is released.

Step 2: Identify and organize the given information
Let's summarize the given information:
- Height of the bridge (h): 84 m
- Velocity of the log (v): 3.6 m/s

Step 3: Analyze the motion of the stone and the log
Since the stone is dropped and the log is moving horizontally, the vertical motion of the stone is independent of the log's motion. This means we can treat the stone's motion as a simple free fall.

Step 4: Solve for the time taken by the stone to fall
We'll use the formula for the time t taken by an object in free fall to fall a given distance h:
h = (1/2) * g * t^2

Here, g represents the acceleration due to gravity, which is approximately 9.8 m/s^2 on Earth.

Rearranging the formula to solve for t:
t^2 = (2h) / g
t = sqrt((2h) / g)

Substituting the given values into the formula:
t = sqrt((2 * 84) / 9.8)
t ≈ 4.532 seconds (rounded to three decimal places)

Therefore, it takes approximately 4.532 seconds for the stone to fall from the bridge.

Step 5: Calculate the horizontal distance
Since the log is moving horizontally at a constant velocity, the horizontal distance covered by the stone during this time will be the velocity of the log multiplied by the time taken by the stone to fall.

Distance = Velocity * Time
Distance = 3.6 m/s * 4.532 s ≈ 16.334 meters

Hence, the horizontal distance between the log and the bridge when the stone is released is approximately 16.334 meters.

Remember to double-check your calculations and units throughout the process.

Sure! I can help you step-by-step with this problem. To find the horizontal distance between the log and the bridge when the stone is released, we need to break down the problem into smaller steps and apply the relevant physics principles.

Step 1: Understand the given information.
- The height of the bridge from which the stone is dropped is 84 meters.
- The log is floating on swiftly moving water and has a constant speed of 3.6 m/s.

Step 2: Determine the time it takes for the stone to fall.
First, we need to determine the time it takes for the stone to fall from the bridge to the log. We can use the equation of motion: h = (1/2)gt^2, where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is time.

Given that h = 84 meters, we rearrange the equation to solve for t:

84 = (1/2) * 9.8 * t^2

Simplifying, we get:

t^2 = 84 * 2 / 9.8
t^2 = 16.98
t ≈ √16.98
t ≈ 4.12 seconds

Therefore, it takes approximately 4.12 seconds for the stone to fall.

Step 3: Find the horizontal distance traveled by the log during the stone's fall.
Since the log is moving with a constant speed of 3.6 m/s, we can calculate the total horizontal distance it travels during the 4.12 seconds.

Distance = Speed x Time
Distance = 3.6 m/s x 4.12 s
Distance ≈ 14.83 meters

Therefore, the log travels approximately 14.83 meters horizontally during the stone's fall.

Step 4: Calculate the horizontal distance between the log and the bridge.
To find the horizontal distance between the log and the bridge, we subtract the horizontal distance traveled by the log from the initial horizontal position of the stone.

Given that the height of the bridge is 84 meters, we can use the equation:

Horizontal Distance = √(Bridge height^2 + Log distance^2)

Horizontal Distance = √(84^2 + 14.83^2)

Horizontal Distance = √(7056 + 219.84)

Horizontal Distance ≈ √7275.84

Horizontal Distance ≈ 85.32 meters

Therefore, the horizontal distance between the log and the bridge when the stone is released is approximately 85.32 meters.

I hope this breakdown helps you solve the problem step by step! Let me know if you have any further questions.