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 magnitude and dicection of the net force acting on Tarzan? b) What is the magnitde and direction of his acceleration?

What would be the equations I should use to solve the problems? I can't find them from my textbook. a) is expose to be 307 N at -22 degrees from the positive x axis. b) is 3.67 m/s^2 at -22 degrees from the postitive x axis.

(a) Two forces act on Tarzan as he leaves the edge of the cliff; the rope tension (at a 22 degree angle to vertical) and gravity (820 N down). They already tell you what the vine tension is, so you just have to "resolve" that into
760 N sin 22 = 284.7 N horizontal and
760 N cos 22 = 704.7 N vertical. The net downward force is
820 - 704.7 = 115.3 N and the net horizontal force is 284.7.
Take the resultant of those for the magnitude of the net force. The ratio of the two forces equals the tangent of the direction angle.

(b) Divide each of those forces by his mass (820 N/9.8 m/s^2 = 83.7 kg) to get the accelerations in the corresponding directions

To solve this problem, you can use Newton's laws of motion and basic trigonometry.

(a) The net force acting on Tarzan can be found by resolving the tension in the vine into horizontal and vertical components. The horizontal component is given by the product of the tension (760 N) and the sine of the angle (22 degrees):

Horizontal component = 760 N * sin(22 degrees) = 284.7 N

The vertical component is given by the product of the tension (760 N) and the cosine of the angle (22 degrees):

Vertical component = 760 N * cos(22 degrees) = 704.7 N

The net force acting on Tarzan is the resultant of these two components. To find the magnitude of the net force, you can use the Pythagorean theorem:

Magnitude of net force = sqrt((284.7 N)^2 + (704.7 N)^2) = 766.8 N

To find the direction of the net force, you can use trigonometry. The ratio of the vertical component to the horizontal component gives you the tangent of the angle:

Tangent of angle = Vertical component / Horizontal component
Tangent of angle = 704.7 N / 284.7 N
Tangent of angle ≈ 2.4747

To find the angle, you can use the inverse tangent function (tan^(-1)):

Angle = tan^(-1)(2.4747)
Angle ≈ 67.6 degrees

Therefore, the magnitude of the net force acting on Tarzan is approximately 766.8 N, and the direction is approximately 67.6 degrees from the positive x-axis (or -22 degrees from the positive x-axis).

(b) To find the acceleration of Tarzan, divide each of the forces (net force, gravity) by his mass:

Acceleration = Net force / Mass = 766.8 N / 83.7 kg ≈ 9.17 m/s^2

The direction of the acceleration is the same as the direction of the net force, which is approximately -22 degrees from the positive x-axis.

Therefore, the magnitude of Tarzan's acceleration is approximately 9.17 m/s^2, and the direction is approximately -22 degrees from the positive x-axis.