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.  

Solution

(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.

Solution

(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

Solution

(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.

Solution

(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°?

Solution

(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?

Solution