Projectile Motion with Wind and Drag

Example: A baseball is hit when it is 3ft above the ground with an initial speed of 152 ft/sec at an angle of 20°. At the instant the ball is hit, an instantaneous gust of wind blows in the horizontal direction directly opposite the direction the ball is taking toward the outfield adding a component of -8.8i (ft/sec) to the ball’s initial velocity. a. Write the position vector and the parametric equations for the path of the baseball.

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

c. Assuming the ball is not caught, find its range and flight time.

The main force affecting the motion of a projectile, other than gravity, is air resistance. This slowing down force is drag force and acts in a direction opposite to the velocity of the projectile. For projectiles moving at low speeds, the drag force is very nearly proportional to the speed and so is called linear drag force.

The baseball above is hit as described above but this time with linear drag slowing it down and not wind. For the temperature and humidity of game day, the drag coefficient k is 0.05. a. Give the parametric equations for the path of the baseball.

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

c. Assuming the ball is not caught, find the range and flight time of the ball. 1. A baseball is hit from 2.5 ft above the ground with an initial speed of 145 ft/sec at an angle of 23°. At the instant the ball is hit, a gust of wind adds a component of -14i (ft/sec) to the initial velocity. A 15ft high fence is 300 ft from home plate in the direction of the flight. a. Give the parametric forms for the path of the ball.

c. Give the range and flight time of the baseball, assuming it is not caught.

d. When is the baseball 20 ft high? How far is the baseball from home plate at that height?

e. Has the batter hit a home run?

2. Consider the baseball problem given above. Assume the temperature and humidity give a drag coefficient of 0.12 and the conditions are otherwise calm (no wind). a. Give the parametric forms for the path of the baseball.

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