MAST10005 Calculus 1
Semester 1, 2014
Assignment 3 cover sheet
Student name:
Student number:
Tutor name:
Tutorial time and day:
Marking table (to be completed by tutor):
Marking categories:
Method (M)
Question 1
Question 2
/2
/1
/1
/2
/2
/1
Answer (A)
Reasoning (R)
Literacy (L)
/1
TOTAL:
/10
Marking criteria
Demonstrating a valid method
required for the problem.
Correct calculations, manipulations,
and final answer.
Clear and correct justification
and explanation.
Clear structure, and correct use
of all mathematical notation.
MAST10005 Calculus 1
Semester 1, 2014
Assignment 3
Due: 2pm, Monday 31 March.
Late assignments will not be accepted.
Note: You may find a calculator useful for computing some ratios and/or square roots in this
assignment.
1. Secret agent Bames Jond, in his gadget-laden speedboat, needs to stop a bomb exploding on
an island 7 km to the north-east. The bomb will detonate in 21 minutes, but to keep things
exciting he intends to arrive with exactly 1 minute to spare.
(a) If i is the unit vector representing a velocity of 1 km/h east and j is the unit vector
representing a velocity of 1 km/h north, what is the vector representing Jond’s required
velocity?
If a boat has velocity b relative to the water it’s in, and the water is flowing with velocity w
relative to land, then the true velocity (relative to land) of the boat is b + w.
30
(b) After 5 minutes Jond encounters a current flowing due south at √
km/h. To stick to his
2
plan, what must he change his velocity (relative to the water) to?
(c) Unbeknownst to Jond, the evil Flobeld attached a bomb to Jond’s boat which will explode
if the speed (i.e. the magnitude of the velocity) of the boat (relative to the water) exceeds
40 km/h. Will Jond survive?
2. From an alien spaceship Earth is in the direction of the vector (1, −8, −4) and Venus is in the
direction (3, 12, 4). The average alien eye has a field of view of 5π
6 radians. Without using arccos
or calculating any exact angles, determine if an average one-eyed alien on the spaceship could
√
see Earth and Venus at the same time. You may find it helpful to use 3/2 ≈ 0.866.
Assignment Instructions
This assignment is worth a compulsory 2% of your final MAST10005 mark.
Submit your assignment to your tutor’s MAST10005 assignment box, near the north entrance of the
Richard Berry building. You should present your work neatly on A4-sized paper, with your name and
student number on each page, and include this cover sheet at the front.
Full working must be shown in your solutions. Marks will be deducted for incomplete
working, poor mathematical expression, and incorrect mathematical notation.
Full solutions will be uploaded to the LMS after the assignment is due.