If a projectile is fired with an initial velocity of v feet per second at an angle theta with the horizontal, it will follow a parabolic path described by y= -16x^2 divided by v^2(costheta)^2 + xtan(theta). Assume that the projectile is fired from the base of a hill that rises with a constant slope of 1/4. Approximate graphically the total horizontal distance traveled by the projectile. I am stuck. Any help is appreciated
Hi there, this is pretty much a really long solution and I could not solve it here by just typing… I really want to help but they don’t have the option to post a photo…
So you are given a (parabolic) path of the projectile and the slope of 1/4
This slope tells you about the values of cos(theta) and tan(theta) i.e. cos(theta) = 4 divided by root 5 and tan(theta) = 1/4. These come from a right triangle with the adjacent = 4 and the opposite = 1
It would be great if this problem comes with a picture; I guess the answer is a value of x in term of v (velocity).
So now, the velocity is y’ (y prime)… You may want to try differentiate y and set y’ = 1/4, then plug in the values of cos(theta) and tan(theta), and solve for x in term of v…