Finding the intial velocity using vectors

[shemer77]

Homework Statement

a fire hose sprays water with an initial velocity of 40ft/s at an angle of 60 degrees to the horizontal. Find the minimum initial velocity to hit a point on a building 15 feet to the right and 16 feet up.

The Attempt at a Solution

these are my equations but i feel like I am missing something b/c I am not sure how i would solve for velocity
r(t)=(z*cos60)T i + (z*sin(60))-16t^2) j
r'(t)=z*cos60) i + (z*sin(60)-32T) j
r''(t)=-32j

 

[LCKurtz]

Homework Statement

a fire hose sprays water with an initial velocity of 40ft/s at an angle of 60 degrees to the horizontal. Find the minimum initial velocity to hit a point on a building 15 feet to the right and 16 feet up.

The Attempt at a Solution

these are my equations but i feel like I am missing something b/c I am not sure how i would solve for velocity
r(t)=(z*cos60)T i + (z*sin(60))-16t^2) j
r'(t)=z*cos60) i + (z*sin(60)-32T) j
r''(t)=-32j

Your equations look OK, with z as the unknown velocity. Use the x equation to figure out when it will have traveled the 15 feet to the wall. Plug that time into the y equation and see what z must be to make y = 16. And put the exact values of cos(60) and sin(60) in those equations.

 

[shemer77]

thats a lot easier said than done, are you sure that's the way to do it? b/c that math is just ugly and terrible

 

[LCKurtz]

thats a lot easier said than done, are you sure that's the way to do it? b/c that math is just ugly and terrible

Yes, I'm sure. You wind up with a quadratic equation in the unknown z. A few square root signs in the answer never hurt anybody.