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Chapter 4 Motion in a plane Solutions

Question - 11 : -
Rain is falling vertically with a speed of 30 ms-1. A woman rides a bicycle with a speed of 10 ms-1 in the north to south direction. What is the direction in which she should hold her umbrella ?

Answer - 11 : -

So woman should hold her umbrella at an angle of 18°26′ with the vertical, towards south.

Question - 12 : -
A man can swim with a speed of 4 km/h in still water. How long does he take to cross a river 1km wide if the river flows steadily at 3 km/h and he makes his strokes normal to the river current ? How far down the river does he go when he reaches the other bank ?

Answer - 12 : -

Question - 13 : -
In harbour, wind is blowing at the speed of 72 km/h and the flag on the mast of a boat anchored in the harbour along  the N-E direction. If the boat starts moving at a speed of 51 km/h to the north, what is the direct ion of the flag on the mast of the boat ?

Answer - 13 : -

Question - 14 : -
The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 ms-1 can go without hitting the ceiling of the hall ?

Answer - 14 : -

Question - 15 : -
A cricketer can throw a ball to a maximum horizontal distance of 100 m. How much high above the ground can the cricketer throw the same ball ?

Answer - 15 : -

Question - 16 : -
A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and direction of acceleration of the

Answer - 16 : -

Question - 17 : -
An aircraft executes a horizontal loop of radius 1 km with a steady speed of 900 km/h. Compare its centripetal acceleration with the acceleration due to gravity.

Answer - 17 : -

Question - 18 : -
Read each statement below carefully and state, with reasons, if it is true or false:
(a) The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre.
(b) The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point.
(c) The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector.

Answer - 18 : -

(a) False, the net acceleration of a particle in circular motion is along the radius of the circle towards the centre only in uniform circular motion.
(b) True, because while leaving the circular path, the particle moves tangentially to the circular path.
(c) True, the direction of acceleration vector in a uniform circular motion is directed towards the centre of circular path. It is constantly changing with time. The resultant of all these vectors will be a zero vector.

Question - 19 : -  The position of a particle is given by
Where t is in seconds and the coefficients have the proper units for r to be in meters.

(a) Find the ‘v’ and ‘a’ of the particle?

(b) What is the magnitude and direction of the velocity of the particle at t = 2.0 s?

Answer - 19 : -

Question - 20 : -
(a) At what time is the x-coordinate of the particle 16 m? What is the y-coordinate of the particle at that time?
(b) What is the speed of the particle at the time?

Answer - 20 : -

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