Little help with Projectile Motion problem

[sun2k4]

Homework Statement

Mike is playing dart at home. Suppose he releases the dart at 15.0 m/s. His releasing
position is 5cm above the dart board center. The horizontal distance between the release position
and the board is 2.5m. How should Mike aim, i.e., what are the angle α and Yoffset as shown on the
graph below? Keep three significant digits, and you need to use the small angle approximation of
cosα=1 when applicable. This approximation is needed once, and only once.

Homework Equations

Range = (V^2/g) sin 2x

The Attempt at a Solution

I tried to use the above equation to solve for sin2x and was able to, but I cannot figure out how calculate the angle without assuming a parabola (the above equation does assume that) because there is a 5cm Y difference between launching point and the point where the dart hits the target, could anyone try to guide me in the right direction here? Any input would be really appreciated

 

[gneill]

The range equation that you quote is only applicable when the starting height is equal to the landing height. This is not the case here.

I'm afraid you'll have to write the equations of motion and "do the math".

 

[sun2k4]

Hi gneill, thank you very much for your answer, could you explain a little bit more? would you be referring to the position functions in terms of time?

 

[gneill]

Hi gneill, thank you very much for your answer, could you explain a little bit more? would you be referring to the position functions in terms of time?

Yes. The "usual" projectile motion equations.