An airforce plane is ascending vertically at the rate of `100 (km)/h`. If the radius of the earth is `r` km, how fast is the area of the earth, visible from the plane, increasing at 3 minutes after it started ascending?Given that the visible area `A` at height ` h` is given by `A=2pir^2h/(r+h)`

The rate of a reaction is given by rate, r = k [H^+]^n If the rate becomes 100 times when the pH changes from 3 to 1, the order of the reaction is

A plane is in level flight at constant speed and each of its two wings has an area of 25 m^2 . If the speed of the air is 180 km//h over the lower wing and 234 km//h over the upper wing surface, determine the plane’s mass. (Take air density to be 1 kg m^-3 )

A man of height 2m walks at a uniform speed of 5km/h away from a lamp post which is 6m high. Find the rate at which the length of his shadow increases.

Water is flowing at the rate of 3km/h through a circular pipe of 20 cm internal diameter into a circular pipe of into a circular cisten of diameter 10m and depth 2 m. in how much time, will the cistern be filled?

A car A is travelling on a straight level road with a uniform speed of 60 km/h. It is followed by another car B which in moving with a speed of 70 km/h. When the distance between then is 2.5km, the car B is given a deceleration of 20km//h^2 . After how much time will B catch up with A

Ten small planes are flying at a speed of 150km/h in total darkness in an air space that is 20xx20xx1.5 km^3 in volume. You are in one of the planes, flying at random within this space with no way of knowing where the other planes are. On the average about how long a time will elapse between near collision with your plane. Assume for this rough computation that a safety region around the plane can be approximated by a sphere of radius 10m.

A fighter plane flying horizontally at an altitude of 1.5 km with speed 720 km//h passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 600 m s^-1 to hit the plane ? At what minimum altitude should the pilot fly the plane to avoid being hit ? (Take g = 10 ms^2 ).

A circle is the locus of a point in a plane such that its distance from a fixed point in the plane is constant. Anologously, a sphere is the locus of a point in space such that its distance from a fixed point in space in constant. The fixed point is called the centre and the constant distance is called the radius of the circle/sphere. In anology with the equation of the circle |z-c|=a , the equation of a sphere of radius is |r-c|=a , where c is the position vector of the centre and r is the position vector of any point on the surface of the sphere. In Cartesian system, the equation of the sphere, with centre at (-g, -f, -h) is x^2+y^2+z^2+2gx+2fy+2hz+c=0 and its radius is sqrt(f^2+g^2+h^2-c) . Q. Radius of the sphere, with (2, -3, 4) and (-5, 6, -7) as xtremities of a diameter, is