If the radar gun of Exercise 16 is aimed at a car travelling at 90 km / h along a straight road

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If the radar gun of Exercise 16 is aimed at a car travelling...

If the radar gun of Exercise 16 is aimed at a car travelling at $90 \mathrm{~km} / \mathrm{h}$ along a straight road, what will its reading be when it is aimed making an angle of $30^{\circ}$ with the road?

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Key Concepts

Vector Decomposition

Vector decomposition involves breaking a vector into components along specified axes. In the context of measuring speed, the actual velocity of an object is often resolved into a component that is parallel to the instrument's line-of-sight. This process is essential when the object's motion is not aligned with the measurement direction.

Trigonometric Projection

Trigonometric projection uses the cosine function to determine the component of a vector in the direction of an angle. When the line-of-sight is at an angle to the object's direction of motion, the measured speed is the product of the true speed and the cosine of that angle, effectively capturing only the portion of the velocity along the line-of-sight.

Line-of-Sight Measurement

Line-of-sight measurement refers to the principle that instruments like radar guns can only measure the component of velocity directly along the line connecting the observer and the object. This concept is critical because if the measuring device is angled relative to the object's path, the reading will be lower than the actual speed, corresponding to the projected component.

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