An arrow has an initial launch speed of 18m/s. If it must strike a target 31m away at the same elevation what?

Question

is the projection angle?

Answer 1

if you asked this physics question about two months ago, i would've been able to answer this for you, but i can't remember how to do it or the equation...sorry

Answer 2

You need trigonometry and physics to solve this problem.
Understanding calculus would help you to see why it works, but it isn't critical.

You need to break down the launch speed into horizontal and vertical components. The vertical component will be 18 times sinx (where x is the projection angle). The horizontal component will be 18 times cosx.

The time to the target is 31 divided by the horizontal component of the launch velocity.

And here's the critical point:
The time that the arrow will take to reach its highest point and then return to its original elevation is 2 times the vertical component divided by 9.8 m/s^2. (The divisor is the acceleration of gravity. First gravity reduces the vertical component to zero. Then it increases it back to the original velocity, but now in a downward direction. That's why you multiply by 2.)

If you followed each of those steps, you can write an expression for the time to the target (as a function of cosx) and an expression for the time the arrow takes to return to its initial elevation (in terms of sinx). Since these two times have to be equal (i.e., the arrow returns to its initial height just as it reaches the target), you set the two expressions equal to each other. Then use trigonometry to solve for the value of x that makes it work. That will be the projection angle.

Good luck.

Answer 3

It never hits the target.
"If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless." (Aristotle Physics VI:9, 239b5)

Answer 4

It should be 34.90 degrees neglecting air resistance. Use the horizontal positioning equation and the vertical positioning equation to find the x-value.
Good luck from here.