2-Dimensional Projectile Motion question

[chroncile]

Homework Statement

A skydiver's parachute has malfunctioned and she is falling at a constant speed of 20 m/s straight down. Fortunately there is an airbag directly below her. Unfortunately, it is not inflated. The switch to inflate the airbag is 30 m to the east of the airbag. If she can throw a wrench eastward with the right speed, it will accelerate down ahead of her (her speed is constant due to air resistance) and hit the switch, triggering the inflation of the airbag. She throws the wrench when she is 200 m above the ground.

How fast should she throw the wrench? [Note, the wrench will initially have a vertical velocity equal to that of the skydiver]

Homework Equations

vf² = vi² + 2ad

The Attempt at a Solution

⌂d = √(200² + 30²)
⌂d = 202.2

vf² = vi² + 2ad
vf² = (20 m/s)² + 2(-9.8)(202.2)
vf² = 400 - 3963.85

The correct answer is 6.42 m/s

 

[Delphi51]

The wrench has motion in 2 dimensions as you note in the title.
So you must make two headings for "horizontal" and "vertical" and use appropriate equations under each heading, keeping the two motions separate. The only quantity that is common to both motions is the time for the fall. Your distance calc doesn't apply because it is partly vertical and partly horizontal and the acceleration is very different in the two directions.