Solving Equations Using Sin/Cos: Projectile Motion

[Let It Be]

1. Trying to understand how to work a given angle into an answer in projectile motion problems.

2. ΔX=ViTf+1/2ATf^2
R=2vi^2sinθcosθ/g

3. Well, I know if you're given say 45° then you would use sin for vertical and cos for horizontal. But beyond that, what are you supposed to do with an angle when given one.

ALSO:
For the first equation, do you substitute Vi for Visinθ or Vicosθ?

 

[SammyS]

It depends upon how θ is defined ! (Answer to both questions)

 

[Let It Be]

It depends upon how θ is defined ! (Answer to both questions)

Can you explain a little more on that?

 

[SammyS]

Can you explain a little more on that?

Sure.

 

[asteriatic]

I would like to provide some clarification and explanation on how to solve projectile motion problems using sin and cos. Projectile motion is a type of motion in which an object is thrown or launched into the air and then moves under the influence of gravity. In order to solve these types of problems, we use equations that involve the trigonometric functions sine and cosine.

In the first equation provided, ΔX represents the displacement or distance traveled in the horizontal direction, Vi is the initial velocity, Tf is the final time, A is the acceleration due to gravity, and g is the gravitational constant. In this equation, we do not substitute Vi for Visinθ or Vicosθ. Instead, we use the value of Vi as it is given in the problem. The angle θ is used in the second equation provided, which calculates the range or horizontal distance traveled by the object. In this equation, we use both sine and cosine since we are taking into account both the vertical and horizontal components of the initial velocity.

When given an angle in a projectile motion problem, it is important to remember that this angle represents the angle at which the object is launched or thrown. This angle is measured from the horizontal axis. In order to solve the problem, we need to break down this angle into its vertical and horizontal components using sine and cosine. For example, if we are given an angle of 30°, we can use sin30° to calculate the vertical component and cos30° to calculate the horizontal component.

In summary, when solving projectile motion problems, we use trigonometric functions such as sine and cosine to break down the initial velocity into its vertical and horizontal components. These components are then used in the equations to calculate the displacement and range of the object. It is important to carefully consider the given angle and use the appropriate trigonometric function for each component.