What Are the Two Possible Launch Angles for a Ball to Land 5 Meters Away?

In summary: The ball starts at the top left and falls to the bottom right. The height of the ball is the distance it falls, or 5 m. So, the horizontal range is 5-m, and the vertical range is 10-m. Therefore, the angle the ball makes with the horizontal is (5-m)/(10-m)*180 degrees, or 30 degrees.
  • #1
jumbo123
5
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Homework Statement


A ball is launched at a speed of 10ms-1. It lands 5m away. Find the two possible values of the angle, θ, which the initial trajectory makes with the horizontal.


Homework Equations


The equations of motion.


The Attempt at a Solution


I realize that I need to find the angle θ and then use sin(180-θ) to find the other possible angle however I do not know how to get it.
 
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  • #2
Interesting problem.

What I'd do is set up a system of equations. You know that the time it takes for the ball the fall and the time it takes for the ball to travel 5 m is the same, right? So, build two position equations and solve for t, then set them equal to each other, leaving only one variable, your angle.

Keeping the angle as a variable, theta, can you come up with two functions, one for the y position and one for the x position? What should the values of these functions as a whole be for each one?

What part of the 10 m/s is horizontal? Which part of the 10 m/s is vertical?
 
  • #3
What I don't understand is how to split to 10m/s into hortizontal and vertical components in order to get the time.
 
  • #4
10 meters per second is the magnitude of the vector. Its the same concept as the hypotenuse of a triangle.
 
  • #5
jumbo123 said:

Homework Statement


A ball is launched at a speed of 10ms-1. It lands 5m away. Find the two possible values of the angle, θ, which the initial trajectory makes with the horizontal.


Homework Equations


The equations of motion.


The Attempt at a Solution


I realize that I need to find the angle θ and then use sin(180-θ) to find the other possible angle however I do not know how to get it.

jumbo123 said:
What I don't understand is how to split to 10m/s into hortizontal and vertical components in order to get the time.

See the "Range and Height" figure at this introductory page:

http://en.wikipedia.org/wiki/Trajectory

.
 

FAQ: What Are the Two Possible Launch Angles for a Ball to Land 5 Meters Away?

What is a steep trajectory?

A steep trajectory is a path or course that has a high slope or incline. In science, it is often used to describe the movement or flight of an object, such as a rocket or projectile, that has a sharp upward angle.

How is a shallow trajectory different from a steep trajectory?

A shallow trajectory is a path or course that has a low slope or incline. In comparison to a steep trajectory, it has a gentler upward angle. This can also be seen in the movement or flight of an object, such as a plane or bird, where the angle of ascent is more gradual.

What factors affect the steepness or shallowness of a trajectory?

The steepness or shallowness of a trajectory is largely influenced by the initial velocity and the angle of launch. A higher initial velocity and a steeper angle of launch will result in a steeper trajectory, while a lower initial velocity and a shallower angle of launch will result in a shallower trajectory.

How are steep and shallow trajectories used in science?

Steep and shallow trajectories are used in various fields of science, such as physics, astronomy, and engineering. They can be used to analyze the motion of objects, predict the flight paths of projectiles, and calculate the orbits of planets and satellites.

What are some real-life examples of steep and shallow trajectories?

Some real-life examples of steep trajectories include the launch of a rocket into space, the flight of a ski jumper, and the path of a thrown baseball. Examples of shallow trajectories include the flight of a frisbee, the trajectory of a golf ball after being hit, and the movement of a paraglider.

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