Horizontal Range Homework: 45° & 30° Angles

In summary, the problem involves finding the ratio of the horizontal ranges at angles 45° and 30° with the same initial speed. Using trigonometry, the horizontal speeds at these angles are determined, but further steps are needed to find the ratio. It is important to clarify the meaning of "horizontal range" as the horizontal distance traveled.
  • #1
Yoruichi
17
0

Homework Statement


A ball is thrown at angles 45° and 30° above the horizontal with the same initial speed. What multiple of the horizontal range at angle 30° is that at angle 45°?

Homework Equations


Trigonometry formula

The Attempt at a Solution


I think that first step is to divide the initial speed into horizontal component and vertical component.
Let the initial speed be u
Horizontal speed of 30° angles : u x cos 30° = 1 / 2 u
Horizontal speed of 45° angles : u x cos 45° = √2 / 2 u

After this I'm not sure what to do next.. Since the question didn't provide time, I can't use the kinetic equation formula.
Can anyone give me a hint about what should I do next?
 
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  • #2
What do you think "horizontal range" means?
 
  • #3
haruspex said:
What do you think "horizontal range" means?
Horizontal distance traveled..
Oh wait, I think I get something..
*edit
 
  • #4
Yoruichi said:
Horizontal distance traveled..
Oh wait, I think I get something..
*edit
Horizontal distance traveled between two points having what relationship?
 

Related to Horizontal Range Homework: 45° & 30° Angles

1. What is horizontal range in relation to 45° and 30° angles?

Horizontal range refers to the distance traveled by an object in a horizontal direction when launched at a certain angle. In this case, it pertains to angles of 45° and 30°.

2. How is horizontal range calculated for 45° and 30° angles?

The formula for calculating horizontal range for any angle is: R = (v^2/g) * sin(2θ), where R is the horizontal range, v is the initial velocity, g is the acceleration due to gravity, and θ is the angle of launch. For 45° and 30° angles, the formula will be R = (v^2/g) * sin(90°) and R = (v^2/g) * sin(60°) respectively.

3. Can you provide an example problem for horizontal range at 45° and 30° angles?

Sure! Let's say an object is launched at an initial velocity of 20 m/s at an angle of 45°. Using the formula R = (v^2/g) * sin(2θ), we can calculate the horizontal range to be R = (20^2/9.8) * sin(90°) = 41.2 meters. Similarly, for an angle of 30°, the horizontal range would be R = (20^2/9.8) * sin(60°) = 24.5 meters.

4. What factors can affect horizontal range at 45° and 30° angles?

The factors that can affect horizontal range at these angles are the initial velocity, the angle of launch, and external forces such as air resistance. Changes in these factors can result in a change in the horizontal range of the object.

5. What real-life applications involve understanding horizontal range at 45° and 30° angles?

Understanding horizontal range at these angles is important in various fields such as sports, engineering, and physics. It is used to calculate the trajectory of a projectile in sports like basketball and baseball, design and launch of rockets in engineering, and predicting the path of a projectile in physics experiments.

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