Calculating horizontal difference in spring-ball situation

AI Thread Summary
To calculate the horizontal distance a ball travels when launched at a 25° angle from a spring, the initial speed of 5.11 m/s must be resolved into horizontal and vertical components using Vx = Vcosθ. The relevant equations include the SUVAT equations, which help analyze motion in both dimensions. The user attempted to solve for horizontal displacement but incorrectly set the final velocity to zero, leading to an erroneous calculation of 1.15 m instead of the correct 2.04 m. To find the correct distance, it's essential to separately analyze the horizontal and vertical motions and apply the appropriate equations for each component. Understanding the relationship between the two components of motion is crucial for solving this problem accurately.
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1.Problem The problem is: calculate the horizontal distance the ball will travel if the same spring is aimed 25° from the horizontal. This is the second part.

The first part was: a small steel ball bearing with a mass of 21 g is on a short compressed spring. When aimed vertically and suddenly released, the spring sends the bearing to a height of 1.33 m. Calculate the speed at which the ball leaves the spring (my correct answer was 5.11 m/s)
2.Relevant equations: Just like the first part I tried using v2=v02+2ax since that still seems relevant. I know I should be incorporating Vx=Vcosθ but I'm not sure how. 3.The attempt at a solution: I set the final velocity to zero and the initial velocity as the answer I had gotten from part one. I set the gravity as acceleration as I had in part one and solved for x (displacement).

0=5.112+2*9.81*x
then x=1.15 m which I know isn't right.

The answer is 2.04 m, I just don't know how to get that.

Also this is my first post so please let me know if I'm missing any information.
 
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You need to break the motion into horizontal and vertical components.
Are you familiar with the SUVAT equations?
What facts do you know about the two components of movement in this problem?
 
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