Projectile motion problem: Calculations for the record distance for the hammer throw

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Homework Statement


The record distance for the hammer throw is about 87m. to achieve this distance, an athlete must produce a centripetal acceleration of nearly 711 m/s^2.
a) Given a radius of 1.21 m calculate the speed of the ball when it is released
b) The athlete lets go when the ball is 2.0 m above the ground moving at an angle of 42 degrees above the horizontal. Determine the range. Ignore any air friction

Homework Equations



The Attempt at a Solution

[/B]
Solved part a and got a velocity of 29.33 m/s. Having an issue with b, i have the solution manuals solution but i don't quite understand why they did certain things in their process. For one, why did they find the final velocity in the y component, why not just immediately find the time? And, they used displacement as -2....which makes sense because its a displacement of -2 metres, but they used positive 9.8 as the acceleration. Why was -9.8 not used and why did they even find the final velocity...why not just go straight to the time using a different kinematic equation? The attached pics contain my solution and the textbooks solution.
 

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kuruman
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The two solutions are equivalent and ought to give the same answer. Which one is used depends on one's personal preference. Having said that, I add that you are correct in pointing out that they should have used -9.8 m/s2. The y-component of the velocity is 19.6 m/s at a height of 2 m above ground. When in drops on the ground it must have a magnitude larger than 19.6 m/s. The solution's claim that it's 18.58 m/s is in error.
 
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