Question

Red Riding Hood sat down to rest and placed her 1.20-kg basket of goodies beside her. A wolf came along, spotted the basket, and began to pull on the handle with a force of 6.40 N at an angle of 25° with respect to vertical. Red was not going to let go easily, so she pulled on the handle with a force of 12.5 N. If the net force on the basket is straight up, at what angle was Red Riding Hood pulling from the vertical? (show work)

Answer 1

117.6°

Step-by-step explanation:

The vertical component of a force directed at some angle α from the vertical is ...

F·cos(α)

We want the vertical components of the wolf's force (Fw) and Red's force (Fr) to total zero. So for some angle from vertical α, Red's force will satisfy ...

Fw·cos(25°) + Fr·cos(α) = 0

cos(α) = -Fw/Fr·cos(25°) ≈ -(6.4 N)/(12.5 N)·0.906308 ≈ -0.464030

α ≈ arccos(-0.464030) ≈ 117.6°

Red was pulling at an angle of about 117.6° from the vertical.

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Additional comment

That's about 27.6° below the horizontal.