Two coast guard stations are located 600 km apart at points A(0,0) and B(0,600). A distress signal from a ship at P is received at slightly different times by two stations. It determined that the ship is 200 km farther from station A than it is from station B. Determine the equation of hyperbola that passes through the location of the help.

Points A and B are 10 km apart and it is determined from the sound of an explosion heard at those points at different times that the location of the explosion is 6 km closer to A than B. Show that the location of the explosion is restricted to a particular curve and find an equation of it.

Suppose that there are two cell phone towers within range of a cell phone. The two towers are located at 6km apart along a straight highway. Running east to west and the cell phone is north of the highway. The signal is 5km from the first tower and sqrt31 km from the second tower. Determine the position of the cell phone north and east of the first tower and how far it is from the highway.

Two charges -q and +q are located at points (0,0,-a) and (0,0,a) respectively. a. What is the electrostatic potential at the points (0,0,z) and (x,y,0)? b. Obtain the dependence of potential on the distance r of a point from the origin which r/a gt gt 1 . c. How much work is done in making a small test charge from the point (5,0,0), (-7,0,0) along the x-axis? Does the answer change if the path of hte test charge between the same points is not along the x-axis?

Suppose the Government has decided to erect a new Electrical Power Transmission Substation to provide better power supply to two villages namely A and B . The substation has to be on the line l. The distances of villages A and B from the foot of the perpendiculars P and Q on the line l are B from the foot of the perpendiculars P and Q on the line l are 3 km and 5 km respectively and the distance between P and Q is 6 km. (i) What is the smallest length of cable required to connect the two villages. (ii) Find the equations of the cable lines that connect the power station to two villages.(Using the knowledge in conjunction with the principle of reflection allows for approach to solve this problem) .

Places A and B are 100 km apart on a highway. One car start from A and another from B at the same time at different speeds. If the car travel in the same direction, they meet in 5 hours, if they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

Lines L_1-=a x+b y+c=0 and L_2-=l x+m y+n=0 intersect at the point P and make an angle theta with each other. Find the equation of a line different from L_2 which passes through P and makes the same angle theta with L_1dot

All the surfaces shown in figure are frictionless. The mass of the car is M, that of the block is mk and the spring has spring constant. Initialy the car and the block are at rest and the spring is stretched through a length x_0 when the system is released. a. Find the amplitude of the simple harmonic motion of the blocks and of the car as seen from the road. b. Find the time periods of the two simple harmonic motions.

Two points are located at a distance of 10 m and 15 m from the source of oscillation. The period of oscillation is 0.05 sec and the velocity of the wave is 300 m//s . What is the phase difference between the oscillation of two points?