What Is the Minimum Angle of Elevation for a Gun to Hit a Target 3000 ft Away?

[laluser]

I am having a problem with a question from my calc 3 class. I don't think there is any calculus involved, however. So the problem goes like this "A shot is fired from a gun with a muzzle velocity of 1200 ft/s is to hit a target 3000 ft away. Determine the minimum angle of elevation of the gun.
Okay so with the vector function equation r(t) = (v0cosøt)i + (v0sinøt -16t²)j
so i set v0cosøt = 3000 and solve for t and then plug that back in for v0sinøt-16t² and set it equal to 0 and solve for ø? That's what i did and get a different angle than the solutions. Could anyone point a finger in the right direction, please? Thank You.

 

[tiny-tim]

Welcome to PF!

… Determine the minimum angle of elevation of the gun.
Okay so with the vector function equation r(t) = (v0cosøt)i + (v0sinøt -16t²)j
so i set v0cosøt = 3000 and solve for t and then plug that back in for v0sinøt-16t² and set it equal to 0 and solve for ø? That's what i did and get a different angle than the solutions. Could anyone point a finger in the right direction, please? Thank You.

Hi laluser! Welcome to PF!

Well, that looks like the right method …

it should give you a quadratic equation with two solutions …

perhaps you picked the wrong one?

If not, show us what equations you did get.

 

[laluser]

Thank you for your reply. I just went back to check my answer and I see that when i was simplifying 3000/100 i said it was 300 instead of 30 giving me much bigger angle. Thanks again!