## Application Problems on Calculus

In this page application problems on calculus we are going to see some practical problems of the topic calculus.

 Questions Solution (1)  A missile fired from ground level rises x meters vertically upwards in t seconds and x = 100t-25t²/2. Find (i) the initial velocity of the missile ,(ii) the time when the height of the missile is a maximum (iii) the maximum height reached (iv) the velocity with which the missile strikes the ground. Solution (2) A particle of unit mass moves so that displacement after t seconds is given by x = cos (2 t - 4). Find the acceleration and kinetic energy at the end of 2 seconds. (K.E = 1/2 m v², m is mass) (3) A stone thrown into still water causes a series of concentric ripples. If the radius of outer ripple is increasing at the rate of 5 cm/sec,how fast  is the area of the distributed water increasing when the outer most ripple has the radius of 12 cm/sec. (4) The radius of a spherical balloon is increasing at the rate of 4 cm/sec. Find  the rate of increases of the volume and surface area when the radius is 10 cm. (5)  A balloon which remains spherical is being inflated be pumping in 90 cm³/sec. Find the rate at which the surface area of the balloon is increasing when the radius is 20 cm. (6) At noon, ship A is 100 km west of ship B. Ship A is sailing east at 35 km/hr and ship B us sailing north at 25 km/hr. How fast is the distance between the ship changing at 4.00 p.m (7) Two sides of a triangle are 4 m and 5 m in length and the angle between them is increasing at the rate of 0.06 rad/sec. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is π/3. (8) Two sides of a triangle have length 12 m and 15 m. The angle between them is increasing at a rate of 2°/min. How fast is the length of third side increasing when the angle between the sides of fixed length is 60°? (9) Gravel is being dumped from a conveyor belt at a rate of 30 ft³/min and its coarsened such that it forms a pile in the shape of cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high?