Tarzan wights 820N, swings from a cliff at the end of a 20m vine that hangs from a high tree limb and initially makes an angle of 22 degrees with the vertical. Immediately after Tarzan steps off the cliff the tension in the cine is 760N. Choose a coordinate system for which the x axis points horizontally away form the edge of the cliff and the y axis points up. a) What is the net force acting on Tarzan in unit-vector notation? b)What is the magnitude and dicection of the net force acting on Tarzan? c) What is the magnitde and direction of his acceleration?

first I found the foce of the vine in unit vector notation. And I got 285i + 705j. What would be the other equations I should use to solve all of the problems?

You only need to add the force of gravity, which is - 820 N j:

F=(285i + 705j - 820j) N =

(285i -115j) N

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To find the net force acting on Tarzan, you need to add the force of the vine (285i + 705j) N and the force of gravity (-820j) N. The unit vector notation separates the forces into their x and y components.

So, the net force (F) acting on Tarzan can be calculated as:

F = (285i + 705j) N + (-820j) N
= 285i + (705j - 820j) N
= 285i - 115j N

Therefore, the net force acting on Tarzan is 285i - 115j N.

Now, to find the magnitude and direction of the net force, you can use the Pythagorean theorem and trigonometry.

The magnitude (|F|) of the net force can be calculated as:

|F| = sqrt[(285)^2 + (-115)^2] N
= sqrt[81225 + 13225] N
= sqrt[94450] N
≈ 307.3 N

The direction (θ) of the net force can be calculated as:

θ = tan^(-1)(-115/285)
= -21.0 degrees (approximation)

Therefore, the magnitude of the net force acting on Tarzan is approximately 307.3 N, and the direction is approximately -21.0 degrees.

Lastly, to find the magnitude and direction of Tarzan's acceleration, you need to divide the net force by Tarzan's mass, which is not given in the question.