A fuzzy die (m = 0.2 kg) hangs from the ceiling of a car. When the car accelerates forward along a horizontal road, the die swings backward so the the string supporting it makes an angle of 4 degree with the vertical. What is the acceleration of the car? HINT: We're not concerned about how the die swung back, only that it has swung back.

Please do it step by step along with the equation please

Help ASAP please!

To find the acceleration of the car, we can consider the forces acting on the fuzzy die. There are two forces acting on the die: the tension force in the string and the force of gravity.

Step 1: Identify the forces acting on the fuzzy die:
- Tension force in the string (upward force)
- Force of gravity (downward force)

Step 2: Set up a free body diagram:
Using the information given, we know that the die swings backward, making an angle of 4 degrees with the vertical. Let's assume that the string makes an angle of θ with the horizontal. The force of gravity acts straight downwards, and the tension force in the string has both vertical and horizontal components.

Step 3: Resolve the forces:
The force of gravity acting on the die is given by the equation:
F_gravity = m * g,
where m is the mass of the die (0.2 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²).

The tension force has two components: T_x (horizontal) and T_y (vertical). Since the die swings back, we have that the tension force is primarily in the horizontal direction, opposing the forward acceleration of the car.

Step 4: Set up the equations:
Using trigonometry, we can relate the angle θ to the angle between the string and the vertical, which is 4 degrees. We have:
tan θ = tan (90° - 4°),
tan θ = tan (86°).

The horizontal component of the tension force is given by:
T_x = T * cos θ,
where T is the tension force in the string.

Step 5: Solve for the tension force:
Rewriting the equation from step 4, we have:
T_x = T * cos(86°).

The vertical component of the tension force is equal to the force of gravity:
T_y = F_gravity = m * g.

Step 6: Relate the acceleration of the car with the tension force:
Since the tension force in the string provides the opposing force to the car's acceleration, we have:
T_x = m * a,
where a is the acceleration of the car.

Step 7: Substitute the values into the equation:
Using the equations from steps 5 and 6, we can substitute the expressions for T_x and T_y:
T * cos(86°) = m * a,
T_y = m * g.

Step 8: Solve for the acceleration of the car:
Now, we can divide the equation from step 7 by T and solve for a:
a = (T * cos(86°)) / m.

Step 9: Substitute known values:
Using the known values, we can now substitute them into the equation:
a = (T * cos(86°)) / 0.2 kg.

Step 10: Calculate the acceleration of the car:
To calculate the acceleration of the car, we need to know the tension force T. Unfortunately, that information is not provided in the question. Without the value of T, we cannot determine the exact acceleration of the car.