Use a tangent function to estimate the grade resistance of a 2200-lb car travelling on a 2.4° grade. Round your answer to the nearest pound.
To estimate the grade resistance of a car using a tangent function, you need to know the weight of the car and the angle of the grade. The grade resistance is the force that opposes the motion of the car up the slope due to gravity.
The formula to calculate the grade resistance using a tangent function is:
Grade Resistance = Weight of the Car * tangent(angle of the grade)
Given:
Weight of the car = 2200 lbs
Angle of the grade = 2.4°
First, convert the angle of the grade from degrees to radians because the tangent function in most programming languages takes the input in radians. The formula to convert degrees to radians is:
radians = degrees * (Pi / 180)
Angle of the grade in radians:
2.4° * (Pi / 180) ≈ 0.0418879 radians
Now, apply the formula to calculate the grade resistance:
Grade Resistance = 2200 lbs * tangent(0.0418879 radians)
To find the tangent of an angle, you can use a scientific calculator that has a tangent function or use the tangent function in programming languages like Python or JavaScript.
For example, in Python, you can use the math library to calculate the tangent:
import math
angle_radians = 0.0418879
grade_resistance = 2200 * math.tan(angle_radians)
rounded_grade_resistance = round(grade_resistance)
The rounded_grade_resistance variable will contain the estimate of the grade resistance of the car, rounded to the nearest pound.