Question

A motor-cycle rider, going 90 km/hour around a
curve with a radius of 100 m must lean at an
angle to vertical. Find the angle at which he
leans​

Answer 1

Answer:

32⁰

Explanation:

radius(r)=100m

acceleration due to gravity(g)=10m/s²

speed of rider(v)=90 km/hr=90×1000÷3600

                          =25m/s²

now

in case of bending

TANФ=v²÷rg

        = 25²÷10×100

        = 0.625

     Ф=Tan⁻¹(0.625)

       = 32°

Answer 2

The angle at which he leans is tan⁻¹(5/8) or, 32°.

A motor cycle rider, going 90 km/hr around a curve with a radius of 100m must lean at an angle to vertical.

We have to find the angle at which he leans.

Speed of motor cycle rider, v = 90 km/hr = 90 × 5/18 = 25 m/s

[ ∵ 1 km/hr = 5/18 m/s ]

radius of the curve, R = 100m

See figure, here we consider the angle at which he leans is A, N is the normal reaction acting on the rider, w is weight of rider, v is speed of rider and R is the radius of curve.

NcosA = W = mg ...(1)

NsinA = mv²/R ....(2)

from equations (1) and (2) we get,

tanA = v²/(Rg) = (25²)/(100 × 10) = 625/1000 = 5/8

⇒ A = tan⁻¹ (5/8) ≈ 32°

Therefore the angle at which he leans is tan⁻¹(5/8) or, 32°.

Also read similar questions : obtain an expression for the angle of lean when a cyclist takes a curved path

https://brainly.in/question/30358

A motor cycle racer takes a round with speed 20 m/s in a curvature of radius of R = 40 m, then the leaning angle of moto...

https://brainly.in/question/23588198