Find the Trajectory's Launch Angle

In summary, to determine the elevation angle at which the cannon should be fired to hit a hilltop target with a horizontal distance of 0.5 miles and vertical distance of 0.25 miles, the formula 2θ=arcsin([g*R]/V^2) can be used. However, to account for the ball landing on the hilltop, the general formula for the projectile, h = xtanθ - 0.5gx2/v2cos2θ, should be used and solved for θ.
  • #1
deveny7
6
0

Homework Statement



A cannon fires at a hilltop target with a muzzle velocity of V = 600 ft/s. The
horizontal and vertical distances to the target are L = 0.5 miles and h = 0.25 miles.
Determine the elevation angle at which the cannon should be fired.

L=2640 ft
h=1320 ft


Homework Equations



2θ=arcsin([g*R]/V^2)

The Attempt at a Solution



2θ=asin([32.2*2640]/360000)

2θ=asin(.2361)

θ=6.8282

This would be the correct angle if the cannon ball were to hit the ground, but the ball is landing on the hilltop. What equation should be used to include the quarter mile in the air?
 

Attachments

  • HW.jpg
    HW.jpg
    18.4 KB · Views: 423
Physics news on Phys.org
  • #2
Use the general formula for the projectile.
h = xtanθ - 0.5gx2/v2cos2θ and solve for θ.
 
  • #3
Thank you!
 

1. What is the definition of "trajectory"?

Trajectory refers to the path or curve that an object follows through space or time, typically due to the influence of external forces such as gravity or air resistance.

2. How do you calculate the launch angle of a trajectory?

The launch angle can be calculated using the equation: angle = arctan (vertical velocity / horizontal velocity). This can also be approximated by measuring the height and horizontal distance of the trajectory and using the formula: angle = arctan (2 * height / horizontal distance).

3. What factors affect the launch angle of a trajectory?

The launch angle of a trajectory is primarily affected by the initial velocity of the object and the angle at which it is launched. Other factors that can influence the launch angle include air resistance, gravity, and external forces such as wind.

4. How does the launch angle affect the distance traveled by an object?

The launch angle directly affects the range or distance traveled by an object. A higher launch angle can result in a longer distance traveled, while a lower launch angle will result in a shorter distance. This is due to the vertical and horizontal components of the initial velocity, with a higher angle providing a greater horizontal component.

5. Can the launch angle be adjusted to optimize the trajectory of an object?

Yes, the launch angle can be adjusted to optimize the trajectory of an object. This is often done in sports such as baseball, where players adjust their swing to achieve the desired trajectory and distance for a home run. In other scenarios, such as projectile motion, the launch angle can be adjusted to hit a target or achieve a specific range.

Similar threads

Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
10
Views
3K
  • Introductory Physics Homework Help
Replies
17
Views
8K
  • Introductory Physics Homework Help
Replies
1
Views
951
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
4K
  • Introductory Physics Homework Help
Replies
2
Views
2K
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
3K
Back
Top