Solving 2D Motion Problems: Where to Start?

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To solve the 2D motion problem involving a cannon firing a ball at a 45° angle with a speed of 283 m/s, start by separating the motion into horizontal and vertical components. Use the equations for horizontal motion, where the initial horizontal velocity is calculated as v_{x0} = v_0 cos(θ), and for vertical motion, where the initial vertical velocity is v_{y0} = v_0 sin(θ). To determine the maximum height, time of flight, and horizontal range, apply the relevant kinematic equations for projectile motion. It is suggested to first calculate the time of flight, as it is crucial for both horizontal and vertical calculations. Understanding these steps will clarify how to approach similar 2D motion problems effectively.
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A cannon barrel is elevated at an angle of 45°. It fires a ball with a speed of 283 m/s. (For the following questions, ignore air resistance.)

(a) What height does the ball reach?
(b) How long is the ball in the air?
(c) What is the horizontal range of the cannon?




Known 2D kinematics equations



No idea how to start. Help me!
 
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I think after doing the other two problems you will have a better understanding of how to do this one.
Let me know if you still need help with this one after.
Hint:
v_{x0} = v_0 cos( \theta )
v_{y0} = v_0 sin( \theta )
 
In grade 11 we do all these 2D motion problems by writing two headings: horizontal and vertical. Then write the formulas you have for the constant speed motion horizontally and the accelerated motion you have vertically. Next, put the known numbers in every formula. Hopefully one of the 3 or 4 formulas can be solved to find something. Finding the time of flight would be really nice because it applies to both the horizontal and vertical parts.
 

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