ENM1600 Engineering Mathematics Assignment 3

• Submit your assignment via EASE as a single PDF file before the deadline. You may resubmit your assignment as long as it is before the deadline. The last submitted version will be marked so please check your assignment carefully before submitting.

• Hand-written work is more than welcome, provided you are neat and legible. Do not waste time type-setting and struggling with symbols. Rather show that you can use correct notation by hand and submit a scanned copy of your assignment. You may also type-set your answers if your software offers quality notation if you wish.

• We expect a high standard of communication. Look at the worked examples in your texts, and the sample solutions in Tutorial Worked Examples to see the level you should aim at. Up to 15% of the marks may be deducted for poor language and notation.

Question 1.

Find each of the following limits: [16 marks]

; .

Question 2. A rocket of mass m = 1000kg is travelling in a straight line for a short time. The distance in metres covered by the rocket during this time is described by the function

r(t) = t3− 3t2 + 6t

where t > 0 is the time in seconds.

[14 marks]

(a) The kinetic energy E of the rocket is given by , where v is the rocket’s speed. Find a function that describes the kinetic energy of the rocket.

(b) Find the kinetic energy of the rocket at time t = 3 seconds.

(c) What is the distance covered by the rocket by time t = 30 seconds?

(d) Find the value of time t when the speed of the rocket is 120ms−1.

(e) Find a function that describes the acceleration of the rocket.

(f) Find the acceleration of the rocket at t = 3 seconds.

(g) Find the time when the rocket’s acceleration is 27ms−2.

Question 3.

Find

[14 marks]

at the point (−2,0), if y3 = x3 + ex sin y + 8.

Question 4.

The work done by a variable force, f(x), is given by [16 marks]

b

W = f (x) dx.

a

(a) Find the indefinite integral of the force

F (x) = 9x 3 √x − 2x 5 + e −2x + 11x

i.e. R f (x)dx.

(b) Hence calculate the exact value of the work done by the force if a = 0 and b = 1 i.e. evaluate the integral

Question 5.

To help find the velocity of particles requires the evaluation of the indefinite [20 marks] integral of the acceleration function, a (t), i.e.

Z v = a(t)dt.

Evaluate the following indefinite integrals:

Z

(a);

Z

(b) (t2 + 1)sin9tdt.

Question 6.

City A and B are separated by a 2km wide river and are located as shown [20 marks] in Figure 1 (not drawn to scale). A road is to be built between city A to B that crosses a bridge straight across the river. Where should the bridge be built (i.e. what is the value of x) so that the road between city A and B is as short as possible? What is the minimum length of the road?

A

Figure 1: Proposed road between A and B.

Total: 100 marks

## Needs help with similar assignment?

We are available 24x7 to deliver the best services and assignment ready within 3-12hours? Order a custom-written, plagiarism-free paper

Get Answer Over WhatsApp Order Paper Now