Edexcel Mathematics Sample paper · Paper 1 · Question 11 · ExamRizz

ExamRizzEdexcel MathematicsMathematics

Sample paper · Paper 1 · Question 11 · 9 marks

11. An archer shoots an arrow. The height, H metres, of the arrow above the ground is modelled by the formula H = 1.8 + 0.4d – 0.002d2 , d  0 where d is the horizontal distance of the arrow from the archer, measured in metres. Given that the arrow travels in a vertical plane until it hits the ground, (a) find the horizontal distance travelled by the arrow, as given by this model. (b) With reference to the model, interpret the significance of the constant 1.8 in the formula. (3) (1) (c) Write 1.8 + 0.4d – 0.002d2 in the form A – B(d – C)2 where A, B and C are constants to be found. (3) It is decided that the model should be adapted for a different archer. The adapted formula for this archer is H = 2.1 + 0.4d – 0.002d2 , d  0 Hence or otherwise, find, for the adapted model (d) (i) the maximum height of the arrow above the ground. (ii) the horizontal distance, from the archer, of the arrow when it is at its maximum height.

Lesson: Laws of Indices