Richard_Iii

Task 4 Practice Paper 1 Question 1: t minutes after a jet engine starts operation, the rate of fuel burn, R kg per minute, is given by the relation . a. Draw a sketch of R as a function of t. b. What is the rate of burn, R, after 7 minutes' c. What value does R approach as t becomes very large' d. Calculate the total amount of fuel burned in the first 7 minutes.¤ Question 2: The rate at which a body cools in air is assumed to be proportional to the difference between its temperature T and the constant temperature S of the surrounding air. This can be expressed by the differential equation where t is the time in hours and k is a constant. a. Show that T = S + Bekt, where B is a constant, is a solution of the differential equation. b. A heated body cools from 80 C to 40 C in 2 hours. The air temperature S around the body is 20 C. Find the temperature of the body after one further hour has elapsed. Give your answer correct to the nearest degree.¤ Question 3: The radius of a circular metal plate is increasing at the rate of 0.01 cm/s when subjected to heat. At what rate is the area increasing when the radius is 5cm' Question 4: i. Show that . ii. The acceleration of a particle moving in a straight line is given by where x metres is the displacement from the origin. Initially, the particle is at the origin with velocity 2 ms–1. Prove that . iii. What happens to v as x increases without bound'¤ Question 5: The path of a projectile fired from the origin O is given by x = Vt cos , y = Vt sin  - 5t2 where V is the initial speed in metres per second and  is the angle of projection as in the diagram and t is the time in seconds. i. Find the maximum height reached by the projectile in terms of V and . ii. Find the range in terms of V and . iii. Prove that the range is maximum when  = 45.¤ ANSWERS Question 1: « a) b) kg/min c) 10 d) 83•5 kg (to 1 d.p.) » Question 2: « a) Proof b) 32 C » Question 3: «0.314 cm2/s. » Question 4: « i) ii) Proof iii) The velocity of the particle approaches zero » Question 5: « i) m ii) m iii) Proof »