Question

A falcon dives toward a pigeon on the ground. When the falcon is at a height of 100 feet the pigeon sees the falcon, which is diving at 220 feet per second. Estimate the time the pigeon has to escape.

Short answer

The pigeon has approximately 0.455 seconds to escape.

Step-by-step solution

Determine Appropriate kinematic equation

The relevant equation for free-fall motion is distance = speed * time, where distance is given in feet, speed is given in feet/sec and time is in seconds.

Substitute the given values

The given values are Distance (d) = 100 feet, and speed (v) = 220 feet/sec. Substitute these into the equation to get 100 = 220 * t.

Solve for time

Rearrange the equation to solve for time (t) gives \( t = \frac{100}{220} \). Compute this to determine the time the pigeon has to escape.

Key concepts

Understanding Free-Fall Motion

Free-fall motion is a fundamental concept in physics that describes the movement of an object under the influence of gravity alone. When an object is in free-fall, it experiences acceleration due to gravity, which on Earth is approximately 9.8 meters per second squared (or 32 feet per second squared).

It's essential to note that this acceleration is constant and acts downward, towards the center of the Earth. In the absence of air resistance, all objects fall at this same rate regardless of their mass. This is why a falcon diving towards the ground accelerates at the same rate as it would if it were simply dropped from rest.

Implications in Real-World Scenarios

When considering real-life situations like a falcon diving, the initial speed of the falcon plays a critical role in determining the duration of its descent. The term 'diving at 220 feet per second' describes the falcon's initial speed. There may also be an initial height from which the falcon dives, which in our case is 100 feet.

Solving for Time in Motion Problems

Solving for time is a common task in kinematic problems. To determine 'how long' an event takes, we can manipulate basic motion equations. The process usually involves isolating the time variable on one side of the equation to make it the subject.

In the scenario described, we have the initial speed and the distance covered during the free-fall. Using the simplified kinematic equation, distance = speed * time, we substitute our known values to find the unknown time variable.

Steps in Solving for Time

• First, identify the equation or formula that relates the variables involved in the motion. In this case, it is distance = speed * time.
• Next, substitute the known values into this equation.
• Finally, rearrange the equation to solve for the unknown time variable.

Applying this to our falcon scenario, solving for time will allow us to understand precisely how much time the pigeon has to react and possibly escape.

The Distance-Speed-Time Relationship

The relationship between distance, speed, and time is fundamental in physics, allowing us to solve many real-world problems. This relationship is often expressed in the straightforward equation:
\[ \text{distance} = \text{speed} \times \text{time} \]
It ties together how far an object travels (distance), how fast it's moving (speed), and how long it's been moving (time).

Applying the Relationship

To apply this equation, if you have any two of the three variables, you can solve for the third. In the falcon example, we knew both the speed of the falcon and the distance it needed to cover to reach the pigeon.

By rearranging this formula to solve for the desired variable, not only can we determine the time required for a given journey — as in finding out how long the pigeon has to escape — but we can also solve for other variables such as distance or speed given different sets of data. This triangular relationship is crucial in understanding motion not only in physics but also in everyday instances of movement.