Question

Find the speed and the velocity of the object. A helicopter is descending for a landing at a rate of 6 feet per second.

Short answer

The speed of the helicopter is approximately 1.83 meters per second and the velocity of the helicopter is approximately -1.83 meters per second, indicating downward motion.

Step-by-step solution

Understand the given parameters

The problem gives us that the helicopter is descending at a rate of 6 feet per second. This gives us the speed but since the helicopter is moving downwards, the direction has to be included to indicate this. Note too that we need to convert this value into meters per second.

Convert speed from feet per second to meters per second

To convert feet to meters, use the conversion factor where 1 foot equals 0.3048 meters. So, multiply 6 feet per second by this conversion factor to obtain the speed in meters per second.

Include direction to find velocity

Velocity is a vector quantity, and as such, it has both a magnitude (speed) and direction. In this case, the helicopter is moving downwards, so the velocity should be -6 feet per second (or, in terms of meters per second, negative of the value calculated in Step 2). This negative sign indicates the downward direction.

Key concepts

Vector Quantity

In physics, understanding the difference between scalar and vector quantities is crucial. Scalar quantities, such as temperature or speed, have only a magnitude. In contrast, vector quantities have both magnitude and direction, which is essential when describing the movement of objects. For instance, when an object moves, it's not enough to know how fast it's going; we also need to know the direction of its motion. This is where velocity comes into play, as it is a vector quantity encompassing both the speed of an object and its direction of travel. When we say a helicopter is descending at 6 feet per second, we're giving its speed. To have its velocity, we must specify the direction - in this case, downward. It's like telling someone how fast you're going on the highway versus pointing out you're going 65 miles per hour north.

Speed Conversion

Different regions and fields of study use various units to measure speed. When working with physics problems, speed conversion can be essential, particularly in settings where standard units may not match. To convert speed, we use conversion factors that relate two units of measure. In the exercise, we transition from feet per second to meters per second with the conversion factor where 1 foot is equivalent to 0.3048 meters. This is achieved by multiplying the speed value (6 feet per second) by the conversion factor. Understanding how to effectively convert units allows for consistent measurements and avoids confusion, especially when collaborating on international projects or comparing results from different sources.

Rate of Descent

When discussing aerial vehicles, such as helicopters, the rate of descent is a term used to describe the vertical speed at which the vehicle is moving toward the ground. It's a particularly important figure for pilots during landing approaches. A controlled rate of descent is necessary for a smooth landing. In our example, the helicopter's rate of descent is 6 feet per second. This represents the speed in the vertical direction; however, it is not yet velocity because it lacks a direction indicator. In aviation, the rate of descent is often carefully monitored to ensure it's within safe operational parameters. These can be affected by multiple factors, including vehicle weight, atmospheric conditions, and pilot input.

Units of Speed

The units of speed used in physics represent how fast an object is moving and are determined by the distance covered over time. Common units include meters per second (m/s), kilometers per hour (km/h), and feet per second (ft/s). The choice of unit often depends on the context; for example, m/s is typically used in scientific studies, while km/h might be more common for vehicle speeds. Knowing how to work with different units of speed is fundamental for physicists and engineers, as the unit must match the context of the given situation, allowing for proper analysis and communication of results. The exercise showcases a unit conversion from feet per second to meters per second to align with the standard scientific units in physics.