Question concerning initial velocity

AI Thread Summary
An athlete's long jump problem involves calculating the take-off speed given a jump angle of 31.6° and a distance of 7.78 m. The initial formula derived for distance appears incorrect, as the correct equation should involve the square of the initial velocity. The discussion highlights the importance of separating vertical and horizontal components to find the total time and then using that to calculate distance. Acknowledgment of algebraic mistakes is noted, emphasizing the need for careful organization in problem-solving. The conversation concludes with a reminder that simple errors can lead to incorrect results.
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Homework Statement



An athlete executing a long jump leaves the ground at a 31.6° angle and travels 7.78 m. What was the take-off speed?

I have tried to solve this question but somehow keep arriving at the wrong answer. The formula that I derived is :

distance=V(initial)*sin^2(theta)/g

Where am I going wrong here? Any help would be appreciated.
 
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Are you computing

distance=V0sin2θ/g

OR

Distance = V02sin2θ/g?

The second one is the one should use.
 
It seems as if I derived the wrong formula via a mistake in my algebra.

Thank you so much!
 
i get a different formula for it.

First take the vertical component, and find the total time taken. Now take the horizontal component of the velocity and multiply by time to find the expression for distance(range)

Substitute and get your answerEDIT: rock.freak answered first, i guess...
 
It seems like I should take more time to organize my thoughts and perform my algebra correctly. Simple mistakes are always my downfall!
 

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