physics
posted by Physics .
I need some help getting a formula. I remember in class u get this really wierd looking equation like
Vicosg((vsin(pheta))/2g)
I think this is what the equatin is when I'm asked to
"Derive a formula for the Range of a projectile based on Vi and the Launch angle, pheta. State when and why is this equation at a maximum."
I'm not exactly sure what it means by maximum or how to derrive the forumula. I think what I wrote above is what i am suppose to eventually get I'm just nore sure how to get that and what it means by maximum

horizontal problem:
u = Vi cos Theta
range = u * time in air
find the time in air with vertical solution:
Vi sin theta = initial speed up
g = acceleration
so
v = Vi sin Theta  g t
h = height = Vi sin Theta * t  .5 g t^2
the height is zero when t = 0 and again when it hits ground at the end of flight
0 = t (Vi sin Theta  .5 g t)
so t = time in air = 2Vi sin Theta /g
so
range = Vi cos Theta * (2/g) Vi sin theta
NOW
if you want to know the angle Theta for maximum range
d range/ d Theta = 0 at maximum
0 = Vi cos Theta*(2/g)Vi cos Theta (2/g) Vi sin theta * Vi sin Theta
or
cos^2 Theta = sin^2 Theta
sin Theta/cos Theta = tan Theta = 1
Theta = 45 degrees
Respond to this Question
Similar Questions

CALC
I am sorry i still don't know how to start. and i am sorry for the problem earlier..it wasn't my fault :( Note that the way students like you are asked to solve this and similar problems is usually not the way people like me solve … 
Physics
I need some help getting a formula. I remember in class u get this really wierd looking equation like Vicosg((vsin(pheta))/2g) I think this is what the equatin is when I'm asked to "Derive a formula for the Range of a projectile based … 
Physics
I'm doing a lab and all i need to know is how to derive an equation I'm accelrating over 5m on a flat surface and people timed it. I can average the time and now the time, distance, my weight and so forth I took down the class notes … 
Physics
so I'm doing the back of this worksheet and on the bottom there's a list of a whole bunch of formulas... I'm asked to find the minimum coefficent of friction if the road was flat of a car which I still don't know how to do and posted … 
AP Physics
I'm trying to derive the formula v^2 = v0^2 + 2a(xx0) were zeros are subscripts my book tells me to derive it this way use the definition of average velocity to derive a formula for x use the formula for average velocity when constant … 
PreCalculus REINY HELP PLEASE
well yay thanks for the answer but i really need the formula lol I tried to derive it on my own but it was a little bit rough lol i need the formula it wasn't in my book and I don't know what the name of the formula would be so i can't … 
Physics, error derivation
I need to derive an error equation for Bohr's model to use in my physics lab this week. I am really bad at calculus, so if anyone can help me that would be really great. the equation is (1/lambda)=R[(1/n^2final)(1/n^2initial)] I've … 
physics, error calculation repost
I need to derive an error equation for Bohr's model to use in my physics lab this week. I am really bad at calculus, so if anyone can help me that would be really great. the equation is (1/lambda)=R[(1/n^2final)(1/n^2initial)] I've … 
Geometry
What formula should be used to derive the equation of a parabola given its focus and directrix? 
Calculus
I apologize if this question is too much to ask on this site, but I am really confused. Any help would be greatly appreciated. The famous formula shown below is called Eulerâ€™s formula, after the Swiss mathematician Leonhard Euler …