During part of its trajectory (which lasts exactly 1 min ) a missile travels at a constant spee

step 1 In this problem we have given the constant speed of missile is 2 ,000 mile per hour. So we will

During part of its trajectory (which lasts exactly 1 min )...

During part of its trajectory (which lasts exactly $1 \mathrm{~min}$ ) a missile travels at a constant speed of $2000 \mathrm{mi} / \mathrm{h}$ while maintaining a constant orientation angle of $20^{\circ}$ from the vertical. (a) During this phase, what is true about its velocity components: $(1) v_{y}>v_{x},$ (2) $v_{y}=v_{x},$ or (3) $v_{y}<v_{x} ?[$ Hint : Make a sketch and be careful of the angle. $]$ (b) Determine the two velocity components analytically to confirm your choice in part (a) and also calculate how far the missile will rise during this time.

Key Concepts

Vector Decomposition

This concept involves breaking a vector into its horizontal and vertical components using trigonometric functions. It is essential when analyzing motion in different directions, as it allows one to separately examine the effects of each component in problems involving trajectories.

Orientation Angle

This refers to the angle at which the vector is directed relative to a specific reference line, such as the vertical or horizontal. Correct interpretation of the angle is crucial because it determines which trigonometric function (sine or cosine) corresponds to the horizontal or vertical component.

Trigonometric Resolution

Using sine and cosine functions to resolve a vector into components provides a method to quantify each component based on the overall magnitude and the orientation angle. In situations where the angle is measured from the vertical, the cosine function typically gives the vertical component, while the sine function gives the horizontal component.

Constant Speed Motion

In cases where an object travels at a constant speed, the lack of acceleration simplifies the analysis since the components of velocity remain constant over time. This allows for straightforward calculations of displacement by multiplying the velocity components by the time interval.

Unit Conversion

Converting units appropriately, such as changing time from minutes to hours, is a critical step in ensuring consistency in calculations. Misalignment of units can lead to errors in determining quantities like displacement or component speeds.

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