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An inquistive student, determined to test the law of gravity for himself, walks to the top of a building og 145 floors, with every floor of height 4 m, having a stopwatch in his hand (the first floor is at a height of 4 m from the ground level). From there he jumps off with negligible speed and hence starts rolling freely. A rocketeer arrives at the scene 5 s later and dives off from the top of the building to save the student. The rocketeer leaves the roof with an initial downward speed v_0 . In order to catch the student at a sufficiently great height above ground so that the rocketeer and the student slow down and arrive at the ground with zero velocity. The upward acceleration that accomplishes this is provided by rocketeer's jet pack, which he turns on just as he catches the student, before the rocketeer is in free fall. To prevent any discomfort to the student, the magnitude of the acceleration of the rocketeer and the student as they move downward together should not exceed 5 g. In Q.1, what would be the approximate retardation to be given by jet pack along for safe landing?

An inquistive student, determined to test the law of gravity for himself, walks to the top of a building og 145 floors, with every floor of height 4 m, having a stopwatch in his hand (the first floor is at a height of 4 m from the ground level). From there he jumps off with negligible speed and hence starts rolling freely. A rocketeer arrives at the scene 5 s later and dives off from the top of the building to save the student. The rocketeer leaves the roof with an initial downward speed v_0 . In order to catch the student at a sufficiently great height above ground so that the rocketeer and the student slow down and arrive at the ground with zero velocity. The upward acceleration that accomplishes this is provided by rocketeer's jet pack, which he turns on just as he catches the student, before the rocketeer is in free fall. To prevent any discomfort to the student, the magnitude of the acceleration of the rocketeer and the student as they move downward together should not exceed 5 g. The correct velocity - time graph for the rocketeer would be

When a current through the medium, an electric field exists as well as a potential which varies in space. Suppose that there is a break in a high - voltage transmission line and the free end of a wire of length L is lying on the ground. An electric current flows through the regions of soil adjoining the conductor. If a man happens to be walking near by a potential difference, which is called the step voltage appears between the points where his feet touch the ground, Consequently, an electric current whose strength depends on this potential difference flows through the man. Let us calculate the step voltage. Since the conductor is quite long, we assume that the current flows from it to the ground in a direction perpendicular to the conductor. The equipotential surfaces are the surfaces of semi-cylinders whose axes coincide with the conductor. Suppose that the man is walking in a direction perpendicular to the conductor with a step of length 'b' the distance between the conductor and the foot closer to it being d. Assuming that the current flows uniformly from the conductor over the semi cylindrical region we obtain the following expression for the current density at a distance from the conductor: j=i/(pirL) In this case , the field strength along the radii perpendicular to the conductor is E_r=j/sigma=l/(pirLsigma) Consequently , the step voltage is V_(st)=int_d^(d+b) Edr =1/(pisigmaL)ln((d+b)/d) For example , If l=500A , d=1 m , b=65 cm and L=30 m we find that V_(st) =270 V. Much higher voltages may appear under other conditions and other shapes of conductors. When a part of a high- voltage transmission line falls on the ground, it creates a hazard

A tank is filled upto a height h with a liquid and is placed on a platform of height h from the ground. To get maximum range x_(m) a small hole is punched at a distance of y from the free surface of the liquid. Then

Assertion: A child in a garden swing periodically presses his feet against the ground to maintain the oscillations. Reason: All free oscillations eventually die out because of the ever present damping force.

An inextensible string AB is tied to a block B of negligible dimensions and passes over a small pulley C so that free end A hangs h unit above the ground on which the block B rests. In this initial position shown in fig. The free end A is h unit below C. if now end A moves horizontally with a velocity v_(0) , obtain an expression for the velocity of the block at any time t.

A uniform plank of mass m, free to move in the horizontal direction only , is placed at the top of a solid cylinder of mass 2 m and radius R. The plank is attached to a fixed wall by mean of a light spring constant k. There is no slipping between the cylinder and the planck , and between the cylinder and the ground. Find the time period of small oscillation of the system.

A rail-road car is moving towards right with acceleration a. A man accelerating toward left with an acceleration of magnitude a//3 w.r.t to car. A dog of mass m is following man A with an acceleration a//3 relative to the car. Observer B on ground is observing the dog and man A. Find the (a) net force experienced by the dog as seen by observer B standing on ground. (b) rate of change of linear momentum of the dog relative to the man A moving on trolley. (c ) pseudo-free on the dog as seen from man A.

An inquistive student, determined to test the law of gravity for himself, walks to the top of a building og 145 floors, with every floor of height 4 m, having a stopwatch in his hand (the first floor is at a height of 4 m from the ground level). From there he jumps off with negligible speed and hence starts rolling freely. A rocketeer arrives at the scene 5 s later and dives off from the top of the building to save the student. The rocketeer leaves the roof with an initial downward speed v_0 . In order to catch the student at a sufficiently great height above ground so that the rocketeer and the student slow down and arrive at the ground with zero velocity. The upward acceleration that accomplishes this is provided by rocketeer's jet pack, which he turns on just as he catches the student, before the rocketeer is in free fall. To prevent any discomfort to the student, the magnitude of the acceleration of the rocketeer and the student as they move downward together should not exceed 5 g. Just as the student starts his free fall, he presses the button of the stopwatch. When he reaches at the top of 100th floor, he has observed the reading of stopwatch as 00:00:06:00. What should be the initial downward speed of the rocketeer so that he catches the student at the top of 100 the floor for safe landing ?

A n-type silicon sample of width 4 xx 10^(-3)m , thickness 25 xx 10^(-5)m and length 6 xx 10^(-2)m carries a current of 4.8 mA when the voltage is applied across the length of the sample. If the free electron density is 10^(22)m^(-3) , then find how much time does it take for the electrons to travel the full length of the sample? Given that charge on an electron e=1.6 xx 10^(-19)C