Harry Potter decides it’s too cold for him to stay in Hogwarts and wants to fly straight south, the heading he should have and the velocity of the broom with respect to the ground are mathematically given as
VR = 20, 699 m/s South
What is the heading he should have and the velocity of the broom with respect to the ground?
Divide horizontal and vertical components of Vs and Vw vectors
For Vs
Vs = Vs cos∅ [s] + Vs Sin∅ [w]
Vs = 18 Co58 [s] + 18 sin∅ [w]
For Vw
Vw = Vw Cos 55' [s] + Vw Sin 55 [E]
5.8333 x Cos 55 (s) + 5-8333 Sin 55 [E]
Vw = 3.3458 [s] + 4.7783 [E]
Resultant velocity VR = Vs + Vw
VR= 18 Coso (s) + 18 sine [w] +3.3458 (5) +42783 (E)
VR = (186030 +3.3458) [5] + (18sing - 4.7183)6]
(Harry Potter) flies south
18sin∅ - 4.7783 18=0
Hence
Sin∅ = 4.7783 18/18
∅ =sin{-1}(4.7783 18/18)
∅ = 15.3943
Harry Potter flies in the direction south to ∅ = $15.3943w]
Hence velocity
VR = (18 cos∅ + 35452) s + 0
VR = (17.3541 +3-3458) s
VR = 20, 69999 m/s South
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