Your CECS graduation tassel hangs from the rear view mirror of your graduation gift, a 1981 DeLorean DMC-12 with Mr. Fusion garbage fusion generator!!! Your tassel hangs plumb or vertical when driving at a constant speed on a level highway. When accelerating you observe the tassel makes an angle of 46 degrees with the horizontal. Determine the magnitude of this acceleration in km/(hour-sec). Enter absolute value only. Do not enter signs.

Draw FBD

Tsin46 = mg
Tcos46 = ma (net force)

a = g cos46/sin46

To determine the magnitude of the acceleration in km/(hour-sec), we can use some basic trigonometry and kinematic equations.

First, let's understand the situation. When the car is driving at a constant speed on a level highway, the tassel hangs vertically or plumb. This means the acceleration is zero at this point.

When the car accelerates, the tassel makes an angle of 46 degrees with the horizontal. We need to find the magnitude of this acceleration.

To solve this problem, we can use the following steps:

Step 1: Convert the angle from degrees to radians.
To do this, we use the formula: radians = degrees * π/180.
So, the angle in radians is: π/4 radians.

Step 2: Determine the horizontal component of the acceleration.
Since the tassel makes an angle with the horizontal, we can find the horizontal component of the acceleration using the formula: horizontal acceleration = acceleration * cos(angle).
Substituting the known values, we get: horizontal acceleration = a * cos(π/4).

Step 3: Convert the horizontal acceleration to km/(hour-sec).
Since the question asks for the magnitude of the acceleration in km/(hour-sec), we need to convert the units.

To convert acceleration from m/s^2 to km/(hour-sec), we use the following conversion factors:
1 m/s^2 = (3.6 km/h) / 3600 sec.

Multiplying the horizontal acceleration by the conversion factor, we get: horizontal acceleration in km/(hour-sec) = horizontal acceleration * (3.6 km/h) / 3600 sec.

Finally, we can calculate the magnitude of the acceleration:

Magnitude of acceleration = absolute value of horizontal acceleration in km/(hour-sec).

Remember to substitute the value of 'a' in the calculations with the magnitude of the acceleration.

Note: The specific value of 'a' is not provided in the question, so you will need to determine it based on the problem context or any other information given.