Shooting into the Wind Suppose that a projectile is fired into a headwind that pushes it back so as to reduce its horizontal speed by a constant amount w. Find parametric equations for the path of the projectile.
The parametric equation for the path of the projectile if the horizontal velocity is decreased by a constant factor
Answer to Problem 6P
The parametric equations for the path of projectile affected by headwind are
Explanation of Solution
Given:
The projectile is fired into a headwind that reduces its horizontal velocity by a constant factor
Calculation:
The path of the projectile has two velocity components, a horizontal and a vertical component.
Suppose that the projectile is fired into the headwind with an initial velocity
Since only the horizontal velocity is decreased by a constant factor
The vertical velocity remains unchanged and is equal to,
The horizontal distance covered by the projectile is,
Substitute
The vertical velocity is not affected by the headwind, but it is affected by the acceleration due to gravity.
Use the second equation of motion to find the vertical distance covered by the projectile as follows.
The second equation of motion is
Substitute
Hence, the parametric equations for the path of projectile affected by the headwind are
Chapter 8 Solutions
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