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Chapter 3: Problem 7

Is a projectile's speed constant throughout its parabolic trajectory?

Short Answer

Expert verified
No, a projectile's speed is not constant throughout its parabolic trajectory. While the horizontal component of velocity remains constant, the vertical component changes due to gravity, which leads to the overall speed changing.

Step by step solution

01

Understand projectile motion

Projectile motion follows a parabolic path. This is due to two simultaneous independent displacements: a constant horizontal displacement and a vertical displacement affected by the constant downward acceleration due to gravity. The velocity of a projectile is a vector quantity composed by these two simultaneous velocities.
02

Analyze the horizontal motion

For horizontal motion, there is no acceleration (assuming we neglect air resistance), so the horizontal velocity component (v_x) remains constant throughout the projectile's trajectory.
03

Analyze the vertical motion

In contrast, for vertical motion, the projectile experiences a constant downward force due to gravity. This causes a negative acceleration (known as 'g'), and the vertical velocity component (v_y) changes throughout the trajectory. It decreases while the projectile goes upwards, becomes zero at the highest point, and then increases in the downward direction on the way down.
04

Combine the velocities

The total velocity of the projectile is a vector formed by combining the horizontal and vertical velocity components. Given that the vertical component is changing due to gravity, and the total velocity is influenced by both the horizontal and vertical components, the total speed of the projectile (the magnitude of the velocity vector) is also not constant.

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Most popular questions from this chapter

Show that, for a given initial speed, the horizontal range of a projectile is the same for launch angles \(45^{\circ}+\alpha\) and \(45^{\circ}-\alpha\)

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