A person sitting in a chair (combined mass 80kg) is attached to a 6m long cable. The person moves in a horizontal circle. The cables angle is 62 degrees below the horizontal. What is the persons speed? Note: the radius of the circle is not 6m.

I really just need and equation all the ones I try just don't work.

The equation you need is:

Speed = √(g x radius x sin(angle))
where g is the acceleration due to gravity (9.8 m/s2).

Therefore, the speed of the person in the chair is:
Speed = √(9.8 x radius x sin(62))

To solve this problem, we can use the concept of centripetal force. The centripetal force acting on an object moving in a circle is given by the equation:

F = (m * v^2) / r,

where F is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius of the circle.

In this case, the gravitational force acting on the person is providing the centripetal force, since the person is attached to the cable. The gravitational force is given by:

F = m * g,

where g is the acceleration due to gravity.

To find the velocity (speed) of the person, we can equate the equations for the centripetal force and the gravitational force:

(m * v^2) / r = m * g.

Since the equation asks for the person's speed, we can eliminate the mass (m):

v^2 / r = g.

Now, to find the speed, we need to express the radius (r) in terms of the given information. We are given that the cable is 6m long and that its angle below the horizontal is 62 degrees. This forms a right-angled triangle, with the cable as the hypotenuse and the horizontal distance as the adjacent side. So, we can use trigonometry to find the radius.

cos(angle) = adjacent / hypotenuse,
cos(62) = r / 6,
r = 6 * cos(62).

Finally, substitute the radius into the equation:

v^2 / (6 * cos(62)) = g.

Rearrange the equation to solve for v:

v^2 = (6 * cos(62)) * g,
v = √((6 * cos(62)) * g).

Plugging in the value of the acceleration due to gravity (approximately 9.8 m/s^2) and calculating the expression will give you the velocity (speed) of the person.

To find the person's speed, we can use the principle of circular motion. The person is moving in a horizontal circle, so there must be a centripetal force acting towards the center of the circle.

First, let's find the radius of the circle. We know that the length of the cable is 6m, and the angle of the cable with the horizontal is 62 degrees. The horizontal component of the cable's length, which forms the radius of the circle, can be found using trigonometry.

Using the cosine function:
cos(62 degrees) = adjacent side / hypotenuse
cos(62 degrees) = radius / 6m

Rearranging the equation to solve for the radius:
radius = 6m * cos(62 degrees)

Now that we have the radius, we can move on to finding the speed. The centripetal force (Fc) is given by the equation:

Fc = m * v^2 / r

Where:
m = mass of the person (80kg)
v = speed of the person
r = radius of the circle

The weight of the person is acting as the centripetal force, and it can be calculated as:

Weight = m * g

Where:
m = mass of the person (80kg)
g = acceleration due to gravity (approximately 9.8m/s^2)

Since the weight is acting as the centripetal force, we can equate the two equations:
Fc = Weight

m * v^2 / r = m * g

Now, we can solve for the speed (v):

v^2 = r * g
v = sqrt(r * g)

Substituting the values we have:

v = sqrt((6m * cos(62 degrees)) * 9.8m/s^2)

Calculating this equation will give you the person's speed. Remember to convert the angle from degrees to radians if your calculator works in radians.