Verified answer

who came up with this question?

i don't think it's the case.

due to earth's gravitational pull our projectile is going to have a parabolic path.

thus the equation would be of the form:

P(x) = - (ax^2 + bx + c)

note: the negative comes from the fact that the parabola opens downward.

for the sake of argument, let's consider the origin to be the point at which we released the projectile, so that c = 0, this had no significance for our cause anyway.

we have:

P(x) = -ax^2 - bx

next we're going to need to convert from rectangular to polar...

r*sin(B) = - a*(r*cos(B))^2 - b*r*cos(B)

sin(B) = -a*r*cos^2(B) - b*cos(B)

let cos(B) = m

m / 1 = adj / hyp

then sin(B) = sqrt(1 - m^2)

and our problem becomes...

sqrt(1 - m^2) = - a*r*m^2- b*m

========================================

1 - m^2 = (a^2 * r^2)*m^4 + (2a*b*r)*m^3 + (b^2*m^2)

we have r = hypotenuse = 1

1 - m^2 = (a^2)*m^4 + (2a*b)*m^3 + (b^2*m^2)

0 = (a^2)*m^4 + (2a*b)*m^3 + (b^2 + 1)*m^2 - 1

there are four answers for m in the equation...

after finding those answers, you would then solve m = arcos(B)

if your statement was true, we would yield B = 45 degrees.

to discover the underlying rationalization for this, detect that @ 40 5 stages the two the X & Y Velocities initiate at .707 of the launch speed. So for a hundred m/s launch Yvel = 70.7 m/s and Xvel = 70.7 m/s. With an Yvel of any fee the rigidity of gravity reduces it to 0 in some elapsed time, in our case of 70.7, that's 70.7 / 9.8 = 7.214 seconds. Now the hollow traveled up could be calculated via utilising taking the classic speed of 70.7 m/s to 0.0 m/s = 70.7 / 2 = 35.35 m/s situations 7.214 seconds = 255 meters up. Now indoors the propose time the X determination = Xvel x time = 70.7 x 7.214 = 510 meters. together using fact the Y action returns to that's commencing off factor the X action retains on for yet yet another 510 meters for a complete of Xrange = 1020 meters together as Yheight retains to be at 255 meters, for this reason outstanding advance good right into a million/4 determination.

let Θ= angle of projectile and u=initial velocity

break the velocity into 2 components that is the horizontal and vertical velocity

use trig to express the velocities in terms of Θ

so let horizontal velocity = Vx and vertical velocity=Vy

then Vx=ucosΘ and Vy=usinΘ

find the time taken to reach max. height where v=0

so v=u+at where a=-g

0=usinΘ-gt make t the subject

t=usinΘ/g

now find the total distance travelled horizontally

so the total time is 2usinΘ/g (since the projectile is of parabolic shape multiply 2 with the time taken for it to reach max. height)

so d=st

= ucosΘ(2usinΘ/g)

=u^2sinΘcosΘ/g

use your knowlegde of trig indentities 2sinΘcosΘ=sin2Θ

now d=u^2sin2Θ/g

use your knowlegde of circle functions

let sin2Θ=1

2Θ=90

Θ=90/2=45

therefore Θ=45 degrees