2-Dimensional Projectile Motion question

In summary, a skydiver needs to throw a wrench with a speed of 6.42 m/s eastward when she is 200 m above the ground in order to hit a switch 30 m away and trigger the inflation of an airbag directly below her. This is calculated using the equation vf2 = vi2 + 2ad and taking into account the different accelerations in the horizontal and vertical directions.
  • #1
chroncile
35
0

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
 
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  • #2
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.
 

FAQ: 2-Dimensional Projectile Motion question

1. What is two-dimensional projectile motion?

Two-dimensional projectile motion refers to the motion of an object in a two-dimensional space, where the object is only affected by gravity and air resistance. This type of motion is commonly seen in objects that are thrown or launched into the air, such as a ball being thrown or a rocket being launched.

2. How is two-dimensional projectile motion different from one-dimensional projectile motion?

In one-dimensional projectile motion, the object only moves along a single axis, typically the vertical axis. In two-dimensional projectile motion, the object moves along both the horizontal and vertical axes, resulting in a curved path known as a parabola.

3. What factors affect two-dimensional projectile motion?

The factors that affect two-dimensional projectile motion include the initial velocity, the angle of launch, the mass and shape of the object, and external forces such as air resistance and wind.

4. How is the trajectory of a projectile calculated?

The trajectory of a projectile can be calculated using mathematical equations such as the kinematic equations and the equations of motion. These equations take into account the initial velocity, angle of launch, and other factors to determine the path of the projectile.

5. What are some real-life applications of two-dimensional projectile motion?

Two-dimensional projectile motion is commonly seen in sports, such as throwing a football or shooting a basketball. It is also used in engineering and physics, such as calculating the trajectory of a rocket or the path of a bullet.

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