Answer:
Angle = 1.07°
Explanation:
Total acceleration consists of translational acceleration (a) which is tangential and centripetal acceleration which is (radial).
Now, Tangential and radial acceleration are always perpendicular to each other. Thus, in a triangle system they are opposite and adjacent sides. From trigonometric ratios,
Opposite/Adjacent = tanθ
Now centripetal acceleration is given as v²/r
Thus, the angle to the radial is given as;
tanθ = translational acceleration/centripetal acceleration
So, tanθ = a/(v²/r) = ar/v²
Thus, θ = tan^(-1)(ar/v²)
Now, Distance of one round of circular motion of 'r' radius
= circumference of circle = 2πr
N = number of trips car makes around the circle
Thus,
total distance = 2πrN
Now, from equation of motion, we know that v² = u² + 2as
Where s is total distance and u is initial velocity which is zero in this case.
Thus, v² = 0² + 2as
Making s the subject;
s = v²/2a
Thus,
2πrN = v²/2a
So let's simplify to bring out ar/v² which is what we will use to calculate the angle. So,
2πrN x 2a = v²
4πN(ar) = v²
Thus, ar/v² = 1/(4πN)
From the question, N = 4.25
Thus,
ar/v² = 1/(4π x 4.25) = 0.0187
From earlier, we saw that the angle is given by;
θ = tan^(-1)(ar/v²)
Thus, θ = tan^(-1)(0.0187)
θ = 1.07°
