18. Exercises - Revision history

Ian at 17:14, 27 March 2011

2011-03-27T17:14:08Z

←Older revision		Revision as of 17:14, 27 March 2011
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	<math>t=\text{ 2}</math>.		<math>t=\text{ 2}</math>.

-	c) Find the magnitude of the resultant force on the particle ~~as a function of <math>t</math>~~.	+	c) Find the magnitude of the resultant force on the particle.

Ian at 17:11, 27 March 2011

2011-03-27T17:11:08Z

←Older revision		Revision as of 17:11, 27 March 2011
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	seconds is given by,		seconds is given by,

-	<math>s=36{{t}^{2}}-2{{t}^{3}}</math>	+	<math>s=18{{t}^{2}}-{{t}^{3}}</math>

	This expression only applies until the acceleration of the dragster becomes zero for the first time.		This expression only applies until the acceleration of the dragster becomes zero for the first time.

Ian at 16:59, 27 March 2011

2011-03-27T16:59:52Z

←Older revision		Revision as of 16:59, 27 March 2011
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	b) Find the time when the velocity is zero.		b) Find the time when the velocity is zero.

-	c) Find the magnitude of the resultant force on the particle ~~at this time~~.	+	c) Find the magnitude of the resultant force on the particle.

	</div>{{#NAVCONTENT:Answer a\|Answer 18.2a\|Answer b\|Answer 18.2b\|Answer c\|Answer 18.2c\|Solution a\|Solution 18.2a\|Solution b\|Solution 18.2b\|Solution c\|Solution 18.2c}}		</div>{{#NAVCONTENT:Answer a\|Answer 18.2a\|Answer b\|Answer 18.2b\|Answer c\|Answer 18.2c\|Solution a\|Solution 18.2a\|Solution b\|Solution 18.2b\|Solution c\|Solution 18.2c}}

Ian at 20:03, 7 October 2010

2010-10-07T20:03:56Z

←Older revision		Revision as of 20:03, 7 October 2010
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	metres, is given by:		metres, is given by:

-	<math>\mathbf{r}=~~\left~~( 40t ~~\right~~)\mathbf{i}+( 3{{t}^{2}}+20t )\~~mathbf~~{j}\~~text~~{ }</math>	+	<math>\mathbf{r}=( 40t )\mathbf{i}+( 3{{t}^{2}}+20t )\text{ }\mathbf{j}</math>

	The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are that are directed horizontally and vertically respectively. The aeroplane is initially at ground level.		The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are that are directed horizontally and vertically respectively. The aeroplane is initially at ground level.

Ian at 20:01, 7 October 2010

2010-10-07T20:01:04Z

←Older revision		Revision as of 20:01, 7 October 2010
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	metres, is given by:		metres, is given by:

-	<math>\mathbf{r}=\left( 40t \right)\mathbf{i}+~~\left~~( 3{{t}^{2}}+20t ~~\right~~)\mathbf{j}\text{ }</math>	+	<math>\mathbf{r}=\left( 40t \right)\mathbf{i}+( 3{{t}^{2}}+20t )\mathbf{j}\text{ }</math>

	The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are that are directed horizontally and vertically respectively. The aeroplane is initially at ground level.		The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are that are directed horizontally and vertically respectively. The aeroplane is initially at ground level.

Ian at 18:57, 7 October 2010

2010-10-07T18:57:19Z

←Older revision		Revision as of 18:57, 7 October 2010
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	<math>t=\text{ 2}</math>.		<math>t=\text{ 2}</math>.

-	c) Find the magnitude of the resultant force on the particle ~~when~~	+	c) Find the magnitude of the resultant force on the particle as a function of <math>t</math>.
-	<math>t~~=\text{ 6}~~</math>.	+

Ian at 14:48, 17 November 2009

2009-11-17T14:48:42Z

←Older revision		Revision as of 14:48, 17 November 2009
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	d) Show that the acceleration of the boat is constant and state the direction of the acceleration.		d) Show that the acceleration of the boat is constant and state the direction of the acceleration.

		+	</div>{{#NAVCONTENT:Answer a\|Answer 18.8a\|Answer b\|Answer 18.8b\|Answer c\|Answer 18.8c\|Answer d\|Answer 18.8d\|Solution a\|Solution 18.8a\|Solution b\|Solution 18.8b\|Solution c\|Solution 18.8c\|Solution d\|Solution 18.8d}}


-	</div>{{#NAVCONTENT:Answer a\|Answer 18.8a\|Answer b\|Answer 18.8b\|Answer c\|Answer 18.~~8c\|Answer d\|Answer 18.8d~~\|Solution a\|Solution 18.8a\|Solution b\|Solution 18.8b\|Solution c\|Solution 18.~~8c\|Solution d\|Solution 18.8d~~}}	+	===Exercise 18.9===
		+	<div class="ovning">
		+
		+	The position vector,
		+	<math>\mathbf{r}</math>
		+	metres, of a particle at time
		+	<math>t</math>
		+	seconds is given by:
		+
		+	<math>\mathbf{r}=({{t}^{2}}-t+5)\mathbf{i}+({{t}^{3}}-12{{t}^{2}}+45t+17)\mathbf{j}</math>
		+
		+	The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are horizontal and vertical unit vectors respectively. The mass of the particle is 3 kg.
		+
		+	a) Find an expression for the velocity of the particle at time
		+	<math>t</math>.
		+
		+	b) Find the times when the particle is moving parallel to the ground.
		+
		+	c) Find an expression for the resultant force acting on the particle at time
		+	<math>t</math>.
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 18.9a\|Answer b\|Answer 18.9b\|Answer c\|Answer 18.9c\|Solution a\|Solution 18.9a\|Solution b\|Solution 18.9b\|Solution c\|Solution 18.9c}}

Ian at 14:43, 17 November 2009

2009-11-17T14:43:03Z

←Older revision		Revision as of 14:43, 17 November 2009
Line 172:		Line 172:

	c) Show that the acceleration of the aeroplane is constant and state its magnitude.		c) Show that the acceleration of the aeroplane is constant and state its magnitude.
-


	</div>{{#NAVCONTENT:Answer a\|Answer 18.7a\|Answer b\|Answer 18.7b\|Answer c\|Answer 18.7c\|Solution a\|Solution 18.7a\|Solution b\|Solution 18.7b\|Solution c\|Solution 18.7c}}		</div>{{#NAVCONTENT:Answer a\|Answer 18.7a\|Answer b\|Answer 18.7b\|Answer c\|Answer 18.7c\|Solution a\|Solution 18.7a\|Solution b\|Solution 18.7b\|Solution c\|Solution 18.7c}}
		+
		+
		+	===Exercise 18.8===
		+	<div class="ovning">
		+
		+	A boat moves so that its position vector,
		+	<math>~\mathbf{r}</math>
		+	metres, at time
		+	<math>t</math>
		+	seconds is given by
		+	<math>\mathbf{r}=\left( 2t-\frac{{{t}^{2}}}{10} \right)\mathbf{i}+2t\mathbf{j}</math>
		+
		+	The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are directed east and north respectively.
		+
		+	(a) Find the time when the boat is due north of its initial position.
		+
		+	b) Find an expression for the speed of the boat at time
		+	<math>t</math>.
		+
		+	c) Find the time when the boat is travelling north.
		+
		+	d) Show that the acceleration of the boat is constant and state the direction of the acceleration.
		+
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 18.8a\|Answer b\|Answer 18.8b\|Answer c\|Answer 18.8c\|Answer d\|Answer 18.8d\|Solution a\|Solution 18.8a\|Solution b\|Solution 18.8b\|Solution c\|Solution 18.8c\|Solution d\|Solution 18.8d}}

Ian at 14:34, 17 November 2009

2009-11-17T14:34:41Z

←Older revision		Revision as of 14:34, 17 November 2009
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	===Exercise 18.7===		===Exercise 18.7===
	<div class="ovning">		<div class="ovning">
		+
		+	An aeroplane moves so that at time
		+	<math>t</math>
		+	seconds, its position vectors,
		+	<math>\mathbf{r}</math>
		+	metres, is given by:
		+
		+	<math>\mathbf{r}=\left( 40t \right)\mathbf{i}+\left( 3{{t}^{2}}+20t \right)\mathbf{j}\text{ }</math>
		+
		+	The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are that are directed horizontally and vertically respectively. The aeroplane is initially at ground level.
		+
		+	a) Find the time when the height of the aeroplane is 500 metres.
		+
		+	b) Find the speed of the aeroplane at this time.
		+
		+	c) Show that the acceleration of the aeroplane is constant and state its magnitude.



	</div>{{#NAVCONTENT:Answer a\|Answer 18.7a\|Answer b\|Answer 18.7b\|Answer c\|Answer 18.7c\|Solution a\|Solution 18.7a\|Solution b\|Solution 18.7b\|Solution c\|Solution 18.7c}}		</div>{{#NAVCONTENT:Answer a\|Answer 18.7a\|Answer b\|Answer 18.7b\|Answer c\|Answer 18.7c\|Solution a\|Solution 18.7a\|Solution b\|Solution 18.7b\|Solution c\|Solution 18.7c}}

Ian at 14:31, 17 November 2009

2009-11-17T14:31:02Z

←Older revision		Revision as of 14:31, 17 November 2009
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	===Exercise 18.6===		===Exercise 18.6===
	<div class="ovning">		<div class="ovning">
		+
		+	A particle, of mass 5 kg, moves so that its position vector,
		+	<math>\mathbf{r}</math>
		+	metres, at time
		+	<math>t</math>
		+	seconds is given by:
		+
		+	<math>\mathbf{r}=(12-2{{t}^{2}})\mathbf{i}+(10-5{{t}^{2}})\mathbf{j}</math>
		+
		+	The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are perpendicular.
		+
		+	a) Find the position of the particle when
		+	<math>t=\text{ 1}0</math>.
		+
		+	b) Find the speed of the particle when
		+	<math>t=\text{ 2}</math>.
		+
		+	c) Find the magnitude of the resultant force on the particle when
		+	<math>t=\text{ 6}</math>.