Question

Follow-up Suppose the kingfisher dives with an average speed of \(4.6 \mathrm{~m} / \mathrm{s}\) for \(1.4 \mathrm{~s}\) before hitting the water. What was the height from which the bird dove?

Short answer

The height is 6.44 meters.

Step-by-step solution

Identify the Given Values

The average speed at which the kingfisher dives is given as \(4.6 \text{ m/s}\) and the time it dives is \(1.4 \text{ s}\).

Understand the Formula

To find the height from which the bird dove, we can use the formula for distance when speed and time are known: \(d = v \times t\), where \(d\) is distance, \(v\) is speed, and \(t\) is time.

Calculate the Height

Substitute the given values into the formula: the average speed \(v = 4.6 \text{ m/s}\) and the time \(t = 1.4 \text{ s}\). Compute the distance \(d = 4.6 \text{ m/s} \times 1.4 \text{ s} = 6.44 \text{ m}\).

Interpret the Result

The computed distance, \(6.44 \text{ m}\), is the height from which the kingfisher dove before it hit the water.

Key concepts

Average Speed

Average speed is a fundamental concept in kinematics, essential for understanding how quickly an object is moving over a period of time. It can be thought of as the total distance traveled divided by the total time taken. Imagine you're driving: the average speed gives you an idea of how fast you're going overall, even though your speed might vary during the journey.

• Average speed is determined using the formula: \( \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \).
• It is important to note that this measures speed independently of any changes in velocity direction.
• Average speed is scalar, which means it doesn't consider direction, making it different from average velocity, which is a vector quantity.

In the exercise of the diving kingfisher, we were given the average speed directly as 4.6 m/s over the 1.4 seconds duration.

Distance Calculation

Distance calculation is a critical aspect of kinematics, involving determining how far an object travels under given conditions. By knowing the speed of an object and the duration of travel, one can compute the distance using a simple and practical formula:

• The formula for calculating distance is given by \( d = v \times t \), where \(d\) is distance, \(v\) is speed, and \(t\) is time.
• This formula assumes that the speed is constant over the time interval.
• Distance is a scalar quantity, which means it only has magnitude and not direction.

In the given exercise, the kingfisher's dive distance - "the height from which it dove" - is calculated using this formula. With an average speed of 4.6 m/s over a time of 1.4 seconds, the distance turns out to be 6.44 meters.

Formula for Distance and Time

Understanding the relationship between speed, distance, and time is essential in solving kinematics problems effectively. This relationship is often described with the formula:

• \( d = v \times t \), where \(d\) is the distance covered, \(v\) is speed, and \(t\) is the time taken.
• This equation allows you to solve for one variable if the other two are known, making it incredibly versatile.
• In situations where speed is not constant, average speed is used within the formula.

For instance, in the kingfisher's scenario, determining the distance (or height) required rearranging the familiar formula to accommodate the known average speed and time. This formula is foundational in physics and helps simplify the calculation of various motion-related quantities.