Question

A cannonball is fired with initial speed v0 at an angle 30° above the horizontal from a height of 42.9 m above the ground. The projectile strikes the ground with a speed of 1.2v0. Find v0.

Answer 1

Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is 59.0 ∘. Rover exerts a force of 390 N and Fido exerts a force of 240 N .
1 Find the magnitude of the resultant force.

2 Find the angle the resultant force makes with Rover's rope.

Answer 2

Wow. I'm not even sure I can explain this one. Here goes. In x initial is vo cos30, in y, vo sin30. x velocity stays constant y velocity is given by final^2 - initial^2 = 2*9.8*42.9.
Final TOTAL velocity is pythogorean sum of x final and y final. Set that equal to 1.2vo. After some heady math you should end up with vo^2 + 841 = 1.44vo^2. I say heady because at one point you must factor out vo and use the sin^2 + cos^2 = 1.
identity.
Anyway I got 43.7 when all was said and done.