Pcos15-1.5gsin15=0

Question

Solve for p

Answer 1

pcos15-1.5gsin15=0,

pcos15=1.5gsin15,

p=1.5gtan15=1.5g(2-√3)=(3-1.5√3)g.

If g=9.8m/s², p=2.626 m/s², if g=32 ft/s², p=8.574 ft/s².

[tan(30)=2tan(15)/(1-tan²(15). Let t=tan(15). tan(30)=1/√3. So 1/√3=2t/(1-t²), 1-t²=2t√3,

t²+2t√3-1=0, t²+2t√3+3-1=3, (t+√3)²=4, t+√3=±2, t=tan(15)=±2-√3. This is a positive number while -2-√3 implies a negative tangent and angle, so this solution for tan(15) can be rejected in this case.]