## Pradeep Kshetrapal is teaching live on Unacademy Plus

PHYSICS for NEET and JEE Pradeep Kshetrapal Class XI Portion

Chapter 4- Motion in a Plane Numerical on 2-D motion Phy-XI-4-13

Q1. Rain is falling vertically with a speed of 30m/s . A woman rides a bicycle with a speed of 10m/s in the north to south direction in which direction she should hold the umbrella? Solution: velocity of rain is 30 m/s VR 30m/s

Given a woman is moving in a bicycle from north to south with a speed of 10m/s. So, 10m/s We want direction of relative velocity of rain with respect to the woman in the bicycle. When two objects are moving there comes a concept of relative velocity.

The direction of rain Umbrella with respect to bicycleV RC IS is R- . Here, VRc is the direction of velocity of the rain with respect to cycle. So, direction of umbrella is opposite to that.

Let 9 be the angle from the vertical with which the umbrella should be tilted. Umbrella tan =10 an-le)-18.43 . 30 RC 3 The woman should bend her umbrella by 18.43 in forward/ south direction.

Q2. A cyclist is riding with a speed 27 km/h As he approaches a circular turn on the road of radius 80m,he applies brakes and reduces his speed at a constant rate of 0.50 m/s every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?

Solution: aT V' dt dv acP 27km/h-15 m/s Given, tangential acceleration,a,--0.5ms-2 This is retardation.

We know that in circular motion there is one more acceleration is working on it i.e.,centripetal acceleration . cp V' dt dv acP

For angle between vectors is 90% then the resultant is T' aT et We know that 15 15 r 80 64 so, net acceleration is R='| (45)2+92= 0.86 ms-2