User interface language: English | Español

Date May 2017 Marks available 2 Reference code 17M.2.AHL.TZ1.H_11
Level Additional Higher Level Paper Paper 2 Time zone Time zone 1
Command term Calculate Question number H_11 Adapted from N/A

Question

Xavier, the parachutist, jumps out of a plane at a height of h metres above the ground. After free falling for 10 seconds his parachute opens. His velocity, v m s 1 , t seconds after jumping from the plane, can be modelled by the function

v ( t ) = { 9.8 t , 0 t 10 98 1 + ( t 10 ) 2 , t > 10

His velocity when he reaches the ground is 2.8  m s 1 .

Find his velocity when t = 15 .

[2]
a.

Calculate the vertical distance Xavier travelled in the first 10 seconds.

[2]
b.

Determine the value of h .

[5]
c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

v ( 15 ) = 98 1 + ( 15 10 ) 2      (M1)

v ( 15 ) = 19.2   ( m s 1 )      A1

[2 marks]

a.

0 10 9.8 t d t     (M1)

= 490   ( m )      A1

[2 marks]

b.

98 1 + ( t 10 ) 2 = 2.8      (M1)

t = 44.985   ( s )      A1

h = 490 + 10 44.9... 98 1 + ( t 10 ) 2 d t     (M1)(A1)

h = 906  (m )      A1

[5 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 5 —Calculus » SL 5.9—Kinematics problems
Show 91 related questions
Topic 5 —Calculus

View options