Projectile Motion with Linear DragHitting a baseball with

Chapter 13, Problem 38E

(choose chapter or problem)

Problem        38E

Projectile Motion with Linear Drag

Hitting a baseball with linear drag Consider the baseball problem in Example 5 when there is linear drag (see Exercise 37). Assume a drag coefficient but no gust of wind.

a. From Exercise 37, find a vector form for the path of the baseball.

b. How high does the baseball go, and when does it reach maximum height?

c. Find the range and flight time of the baseball.

d. When is the baseball 30 ft high? How far (ground distance) is the baseball from home plate at that height?

e. A 10-ft-high outfield fence is 340 ft from home plate in the direction of the flight of the baseball. The outfielder can jump and catch any ball up to 11 ft off the ground to stop it from going over the fence. Has the batter hit a home run ?

Reference: Exercise 37

The main force affecting the motion of a projectile, other than gravity, is air resistance. This slowing down force is drag force, and it acts in a direction opposite to the velocity of the projectile (see accompanying figure). For projectiles moving through the air at relatively low speeds, however, the drag force is (very nearly) proportional to the speed (to the first power) and so is called linear.

Linear drag Derive the equations

by solving the following initial value problem for a vector r in the plane.

The drag coefficient k is a positive constant representing resistance due to air density, are the projectile’s initial speed and launch angle, and g is the acceleration of gravity.