Vector 2D Problem: Solve for Horizontal Range & Time in Motion

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To solve the problem of a ball fired at an initial speed of 1.70 x 10^3 m/s at a 55-degree angle, one must first break down the initial velocity into horizontal and vertical components using trigonometric functions. The horizontal range can be calculated using the formula R = (v^2 * sin(2θ)) / g, where g is the acceleration due to gravity. The time of flight can be determined using the vertical motion equation, t = (2 * v * sin(θ)) / g. Understanding that this is a kinematics problem rather than a purely vector problem is crucial for applying the correct equations. Mastery of these foundational concepts is essential for solving similar projectile motion problems effectively.
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I would really appreciate it if you could help me out with this type of problem...I'm struggling a bit on the order of work that I need to do.

Problem: The ball is fired from the ground with an initial speed of 1.70 x 10^3 m/s at an initial angle of 55 degrees to the horizontal. Neglecting air resistance, find:

a) The balls horizontal range?
b) The amount of time the ball is in motion?

My Thoughts: I'm not sure which formulas to begin with...I'm still slightly confused on the operations with component and vector projectile problems in 2D.
 
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This type of question is fundamntal. What equations of motion do you use for your foundation?
 
This is a kinematics problem, not a vector problem.
 

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