A dart leaves a toy dart gun with initial velocity of 7.76 m/s, regardless of the angle it is fired. What is the maximum horizontal distance that the dart can travel? Assume that the dart gun is fired at ground level.

Question

anonymous · Answer

You must decide (analyze the system) what the optimal (best) angle from which to fire the dart to achieve maximum horizontal distance.  If fired purely horizontally, then the angle is zero and the dart immediately hits the ground- gravity is always acting on the dart.  If fired vertically, then the angle is 90 and it will go up and down but no horizontal distance.  There is an optimal angle at which the dart will  travel the maximum horizontal distance.

anonymous · Answer

thanks @squoe44oz but is more information needed for this problem?

johnweldon1993 · Answer

Hint* We can just use the general kinematics equation, and derive for Range, to save you some time...

$$\large Range = \frac{v_o ^2 sin(2\theta)}{g}$$

So think..since V is fixed, and g is fixed...what value of $\large \theta$ will give you the maximum value here?

Hint2* When is $\large sin(\theta)$ largest?

anonymous · Answer

okay i got 12.28, is that correct? @johnweldon1993

johnweldon1993 · Answer

Hmm... can I see the work you did?

anonymous · Answer

can you please answer it :(