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Relative Velocity

Q- A motor boat, with its engine on in a running river and blown over by a horizontal wind is observed to travel at 20 km/hr in a direction 530 East of North. The velocity of the boat with its engine on in still water and blown over by the horizontal wind is 4 km/hr Eastward and the velocity of the boat with its engine on over the running river, in the absence of wind is 8 km/hr due South. Find                                         (a) the velocity of the boat in magnitude and direction, over still water in the absence of wind                                                                 (b) the velocity of the wind in magnitude and direction.                                                            

Motion in two dimensions

Q- A bus is running along a highway at a speed of v1 =16 ms-1. A man is at a distance a = 40m from the highway and at a distance b = 196 m from the bus. In what direction should the man run to reach any point on the highway at the same time as the bus or before? The man can run at a speed of v2=4 ms-1.

Solution:

Sound Waves: Open Tube

Q- The fundamental frequency of an open-open tube is 1500 Hz, when it is filled with helium at 0oC. What is the frequency when it is field with air at 0oC?

Solution:

Conservation of energy

Q- An object of mass m starts from rest and slides a distance d down a frictionless incline of angle θ. While sliding, it contacts an unstressed spring of negligible massand force constant k.  The object slides an additional distance x as it is brought momentarily to rest by compression of the spring. Find the initial separation d between object and spring.

Solution:

Heat and Thermodynamics

Q- 0.110 mol of a monatomic gas follows the process shown in the figure.

(a) How much heat energy is transferred to or from the gas during process 1 → 2 ?

(b) How much heat energy is transferred to or from the gas during process 2 → 3?

(c) What is the total change in thermal energy of the gas?

Solution:

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