You shoot off a toy rocket at an angle 20 degrees west of north while the wind is blowing east to west at 10 mph. The rocket's actual speed is (with the wind) is 64.11 mph. What is the actual direction of the rocket?
It seems necessary to know what the initial speed of the rocket is to solve this problem. Can anyone show me why it isn't and what the answer is? Thanks.
Best Answer
You're given, velocity of wind: $$v_w=-10\hat i\;\rm mph$$ velocity of rocket(let speed be x): $$v_r=[x\cos(20^\circ)\hat i-x\sin(20^\circ)\hat j]\;\rm mph$$ velocity of rocket with respect to wind: $$v_r-v_w=v_{r,w}=[(x\cos(20^\circ)+10)\hat i-x\sin(20^\circ)\hat j]\;\rm mph$$ And given that $|v_{r,w}|=64.11\;\rm mph$ can't you get x?: $$[x\cos(20^\circ)+10]^2+[x\sin(20^\circ)]^2=64.11^2$$ solving: $$x=54.62$$