A gymnast weighing 72 kg hangs from a cross bar. His coach pushes him

forward with a force of 38 N and backward with a force of 20 N. The
upward reaction force on the gymnast is 750N. Calculate:
i). The resultant (net) force on the gymnast and
ii). The angle of the resultant force with the hands of the gymnast on
the cross bar. (15 marks)
(Show all the steps. W (Newton) = mg; where g is approximately 10 m/ S2

If they are going to try to teach you physics, I don't understand why they tell you to use the wrong value of g. It should be 9.81 m/s^2, on Earth.

Add the weight force (M*g) to the other three forces and compute the resultant. You have a total of 18 N backwards and 750- M*g up. If you used g = 10, that would be 30 N up.

The magnitude of the resultant is
sqrt[(18)^2 + (30)^2] = 34.99 N

The angle of the resultant arctan 18/30 or 31 degrees backwards from vertical.

To find the resultant force on the gymnast, we need to find the difference between the total force acting forward and the total force acting backward. Let's calculate it step by step:

Given:
Weight of gymnast (W) = 72 kg
Force pushing forward (F forward) = 38 N
Force pushing backward (F backward) = 20 N

i) Finding the Resultant (Net) Force:

1. Calculate the weight of the gymnast (W) using the formula W = mg, where g is the acceleration due to gravity (approximately 10 m/s^2):
W = 72 kg * 10 m/s^2
W = 720 N

2. Calculate the net force by subtracting the force pushing backward from the force pushing forward:
Net Force = F forward - F backward
Net Force = 38 N - 20 N
Net Force = 18 N

Therefore, the resultant (net) force on the gymnast is 18 N.

ii) Finding the Angle of the Resultant Force:

To find the angle of the resultant force with the hands of the gymnast on the crossbar, we need to calculate the angle using trigonometry.

1. Determine the vertical component of the resultant force (F vertical):
F vertical = upward reaction force on the gymnast
F vertical = 750 N

2. Determine the horizontal component of the resultant force (F horizontal):
F horizontal = net force (from part i)
F horizontal = 18 N

3. Calculate the angle using the formula:
Tan(angle) = F vertical / F horizontal

Substitute the values:
Tan(angle) = 750 N / 18 N

Using the inverse tangent (tan^-1) function on a calculator, we can find the angle:
Angle = tan^-1(750 N / 18 N)

Calculating this value gives us the angle of the resultant force with the hands of the gymnast on the crossbar.

Note: Please use a scientific calculator or an online calculator to find the inverse tangent.