Projectile Motion given only distances

In summary, the problem is asking for the speed and angle at which a package should be thrown from a distance of 3.5 m to reach a second-floor window 4.5 m above the ground. The equations of motion can be used to solve for the vertical and horizontal velocities, which can then be used to calculate the speed and angle of the throw. Additional equations and knowledge of the acceleration due to gravity are needed to solve the problem accurately.
  • #1
Bruarios
1
0

Homework Statement


Standing on the ground 3.5 m from the wall of a building, you want to throw a package from your 1.6 m shoulder level to someone in a second-floor window 4.5 m above the ground. At what speed should you throw the package so it just barely reaches the window? At what angle should you throw the package so it just barely reaches the window?


Homework Equations


I looked through all my lecture notes, the book and several websites trying to find some equations that would allow me to solve this but all of them required at least one of the variables that were not given.

vy = v0sinθ0 - gt
y = v0sinθ0t - (1/2)gt2.
x = v0xt
y = xtan(θ0) - gx2/(2v02cos20))

I'm sure I'm missing a few but I don't know which would be needed, hence the post.


The Attempt at a Solution



I tried using trig to find the angle. I got 39.6442° which was incorrect according to the website, so I am stumped.
 
Physics news on Phys.org
  • #2
You solve this with using the equations of motion.

Break the problem up into solving for the y-direction and then the x-direction.

You know the acceleration, g, in the vertical direction, the distance in the vertical direction, and the velocity of the package just to reach the window height would be what ??
From those facts you can calculate the vertical velocity of the package as it leaves your hand.

Here are some equations from a site:
http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html#mot1

( You should familiarize yourself with them, so you don't have to look them up all the time )

Then you can solve for the velocity in the x-direction, for the ball to reach the window horizontally.

From the vertical and horizontal velocities you can then calculate the speed and angle of the package.
 

1. What is projectile motion?

Projectile motion is the motion of an object that is projected into the air and then moves along a curved path under the influence of gravity.

2. Can projectile motion be described using only distances?

Yes, projectile motion can be described using only distances as long as the initial velocity, angle of projection, and acceleration due to gravity are known.

3. What is the formula for calculating the horizontal distance of a projectile?

The formula for calculating the horizontal distance of a projectile is d = v0 * t * cos(theta), where d is the horizontal distance, v0 is the initial velocity, t is the time of flight, and theta is the angle of projection.

4. How does the angle of projection affect the range of a projectile?

The range of a projectile is maximized when the angle of projection is 45 degrees. As the angle increases or decreases from 45 degrees, the range decreases.

5. What factors can affect the distance traveled by a projectile?

The distance traveled by a projectile can be affected by the initial velocity, angle of projection, and air resistance. Other factors such as wind, air density, and launch height can also have an impact on the distance traveled.

Similar threads

  • Introductory Physics Homework Help
Replies
8
Views
2K
  • Introductory Physics Homework Help
Replies
17
Views
16K
  • Introductory Physics Homework Help
Replies
15
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
5K
  • Introductory Physics Homework Help
Replies
25
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
4K
  • Introductory Physics Homework Help
Replies
23
Views
3K
Back
Top