8. Exercises - Versionshistorik

Ian den 14 september 2009 kl. 12.57

2009-09-14T12:57:38Z

← Äldre version		Versionen från 14 september 2009 kl. 12.57
Rad 137:		Rad 137:

	</div>{{#NAVCONTENT:Answer a\|Answer 8.9a\|Answer b\|Answer 8.9b\|Solution a\|Solution 8.9a\|Solution b\|Solution 8.9b}}		</div>{{#NAVCONTENT:Answer a\|Answer 8.9a\|Answer b\|Answer 8.9b\|Solution a\|Solution 8.9a\|Solution b\|Solution 8.9b}}
		+
		+
		+	===Exercise 8.10===
		+	<div class="ovning">
		+
		+	A radio controlled aeroplane has initial position 10<math>\mathbf{k}</math> m and at this time is flying north east with a speed of <math>8\sqrt{2}</math> <math>\text{m}{{\text{s}}^{-1}}</math>. It has an acceleration of
		+	<math>(0.01\mathbf{i}+0.02\mathbf{j}+0.1\mathbf{k})</math>
		+	<math>\text{m}{{\text{s}}^{-2}}</math>. The unit vectors <math>\mathbf{i}</math>, <math>\mathbf{j}</math> and <math>\mathbf{k}</math> are directed east, north and vertically upwards respectively. The aeroplane stops accelerating when it reaches a height of 90 metres.
		+
		+	a) Find the time for which the aeroplane is accelerating.
		+
		+	b) Find the speed of the aeroplane when it stops accelerating.
		+
		+	c) A car drives so that it is always directly below the aeroplane. Find the distance between the initial position of the car and its position when the aeroplane stops accelerating.
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 8.10a\|Answer b\|Answer 8.10b\|Answer c\|Answer 8.10c\|Solution a\|Solution 8.10a\|Solution b\|Solution 8.10b\|Solution c\|Solution 8.10c}}

Ian den 14 september 2009 kl. 12.41

2009-09-14T12:41:37Z

← Äldre version		Versionen från 14 september 2009 kl. 12.41
Rad 122:		Rad 122:

	</div>{{#NAVCONTENT:Answer a\|Answer 8.8a\|Answer b\|Answer 8.8b\|Solution a\|Solution 8.8a\|Solution b\|Solution 8.8b}}		</div>{{#NAVCONTENT:Answer a\|Answer 8.8a\|Answer b\|Answer 8.8b\|Solution a\|Solution 8.8a\|Solution b\|Solution 8.8b}}
		+
		+	===Exercise 8.9===
		+	<div class="ovning">
		+
		+	The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are horizontal and vertical respectively. An arrow is shot so that it starts to move with velocity (<math>15\mathbf{i}+18\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-1}}</math> from the point with position vector 1.5<math>\mathbf{j}</math> m. After 3 seconds it hits a target. Assume that the acceleration of the particle is -10<math>\mathbf{j}</math> <math>\text{m}{{\text{s}}^{-2}}</math> and that the arrow can be modelled as a particle.
		+
		+	a) Find the position of the point where the arrow hits the target.
		+
		+	b) Find the speed of the arrow when it hits the target.
		+
		+
		+
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 8.9a\|Answer b\|Answer 8.9b\|Solution a\|Solution 8.9a\|Solution b\|Solution 8.9b}}

Ian den 14 september 2009 kl. 12.26

2009-09-14T12:26:12Z

← Äldre version		Versionen från 14 september 2009 kl. 12.26
Rad 106:		Rad 106:

	</div>{{#NAVCONTENT:Answer a\|Answer 8.7a\|Answer b\|Answer 8.7b\|Answer c\|Answer 8.7c\|Solution a\|Solution 8.7a\|Solution b\|Solution 8.7b\|Solution c\|Solution 8.7c}}		</div>{{#NAVCONTENT:Answer a\|Answer 8.7a\|Answer b\|Answer 8.7b\|Answer c\|Answer 8.7c\|Solution a\|Solution 8.7a\|Solution b\|Solution 8.7b\|Solution c\|Solution 8.7c}}
		+
		+	===Exercise 8.8===
		+	<div class="ovning">
		+
		+	The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are perpendicular and lie in a horizontal plane. A particle moves from the origin. Its initial velocity was (<math>4\mathbf{i}+6\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-1}}</math> and after 20 seconds its velocity is (<math>24\mathbf{i}+46\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-1}}</math>. The acceleration of the particle is constant.
		+
		+	a) Find the acceleration of the particle.
		+
		+	b) Find the distance of the particle from the origin after accelerating
		+	for 30 seconds.
		+
		+
		+
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 8.8a\|Answer b\|Answer 8.8b\|Solution a\|Solution 8.8a\|Solution b\|Solution 8.8b}}

Ian den 14 september 2009 kl. 12.19

2009-09-14T12:19:20Z

← Äldre version		Versionen från 14 september 2009 kl. 12.19
Rad 89:		Rad 89:

	</div>{{#NAVCONTENT:Answer a\|Answer 8.6a\|Answer b\|Answer 8.6b\|Solution a\|Solution 8.6a\|Solution b\|Solution 8.6b}}		</div>{{#NAVCONTENT:Answer a\|Answer 8.6a\|Answer b\|Answer 8.6b\|Solution a\|Solution 8.6a\|Solution b\|Solution 8.6b}}
		+
		+
		+
		+	===Exercise 8.7===
		+	<div class="ovning">
		+
		+	A football is kicked so that its initial velocity is
		+	(<math>8\mathbf{i}+10\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-1}}</math>. Assume that its acceleration is -10<math>\mathbf{j}</math> <math>\text{m}{{\text{s}}^{-2}}</math>, where the unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are horizontal and vertical unit vectors respectively. Assume that the ball is kicked from the origin, which is on a horizontal surface.
		+
		+	a) After the ball has been moving for ''T'' seconds it hits the ground for the first time. Find ''T''.
		+
		+	b) Find the distance of the point where the ball hits the ground for the first time from the origin.
		+
		+	c) Find the maximum height of ball.
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 8.7a\|Answer b\|Answer 8.7b\|Answer c\|Answer 8.7c\|Solution a\|Solution 8.7a\|Solution b\|Solution 8.7b\|Solution c\|Solution 8.7c}}

Ian den 12 september 2009 kl. 17.16

2009-09-12T17:16:46Z

← Äldre version		Versionen från 12 september 2009 kl. 17.16
Rad 79:		Rad 79:


-	A boat has initial velocity (<math>\mathbf{i}+2\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-1}}</math>. It moves with a constant acceleration, <math>\mathbf{a}</math> ~~<math>\text{m}{{\text{s}}^{-2}}</math>~~ until after 10 seconds its velocity is (<math>6\mathbf{i}-8\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-1}}</math>. The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are directed east and north respectively.	+	A boat has initial velocity (<math>\mathbf{i}+2\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-1}}</math>. It moves with a constant acceleration, <math>\mathbf{a}</math> until after 10 seconds its velocity is (<math>6\mathbf{i}-8\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-1}}</math>. The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are directed east and north respectively.

	(a) Find <math>\mathbf{a}</math> .		(a) Find <math>\mathbf{a}</math> .

Ian den 12 september 2009 kl. 17.12

2009-09-12T17:12:45Z

← Äldre version		Versionen från 12 september 2009 kl. 17.12
Rad 74:		Rad 74:

	</div>{{#NAVCONTENT:Answer a\|Answer 8.5a\|Answer b\|Answer 8.5b\|Solution a\|Solution 8.5a\|Solution b\|Solution 8.5b}}		</div>{{#NAVCONTENT:Answer a\|Answer 8.5a\|Answer b\|Answer 8.5b\|Solution a\|Solution 8.5a\|Solution b\|Solution 8.5b}}
		+
		+	===Exercise 8.6===
		+	<div class="ovning">
		+
		+
		+	A boat has initial velocity (<math>\mathbf{i}+2\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-1}}</math>. It moves with a constant acceleration, <math>\mathbf{a}</math> <math>\text{m}{{\text{s}}^{-2}}</math> until after 10 seconds its velocity is (<math>6\mathbf{i}-8\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-1}}</math>. The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are directed east and north respectively.
		+
		+	(a) Find <math>\mathbf{a}</math> .
		+
		+	(b) The boat then travels with this velocity for a further 40 seconds. Find the distance between the initial and final positions of the boat.
		+
		+
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 8.6a\|Answer b\|Answer 8.6b\|Solution a\|Solution 8.6a\|Solution b\|Solution 8.6b}}

Ian den 12 september 2009 kl. 16.29

2009-09-12T16:29:18Z

← Äldre version		Versionen från 12 september 2009 kl. 16.29
Rad 58:		Rad 58:

	</div>{{#NAVCONTENT:Answer a\|Answer 8.4a\|Answer b\|Answer 8.4b\|Answer c\|Answer 8.4c\|Solution a\|Solution 8.4a\|Solution b\|Solution 8.4b\|Solution c\|Solution 8.4c}}		</div>{{#NAVCONTENT:Answer a\|Answer 8.4a\|Answer b\|Answer 8.4b\|Answer c\|Answer 8.4c\|Solution a\|Solution 8.4a\|Solution b\|Solution 8.4b\|Solution c\|Solution 8.4c}}
		+
		+
		+	===Exercise 8.5===
		+	<div class="ovning">
		+
		+
		+	A light aeroplane has a velocity of 80<math>\mathbf{i}</math> <math>\text{m}{{\text{s}}^{-1}}</math>, as it is moving along a runway. When it takes off it then experiences an acceleration of (<math>\mathbf{i}+4\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-2}}</math> for the first 30 seconds of its flight. The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are directed horizontally and vertically respectively. Assume that the aeroplane is at the origin when it takes off and begins to accelerate.
		+
		+	a) Find expressions for the velocity and position of the aeroplane at time t seconds.
		+
		+	b) Find the speed of the aeroplane when it is at a height of 50 m.
		+
		+
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 8.5a\|Answer b\|Answer 8.5b\|Solution a\|Solution 8.5a\|Solution b\|Solution 8.5b}}

Ian den 12 september 2009 kl. 16.19

2009-09-12T16:19:20Z

← Äldre version		Versionen från 12 september 2009 kl. 16.19
Rad 44:		Rad 44:

	</div>{{#NAVCONTENT:Answer\|Answer 8.3\|Solution\|Solution 8.3}}		</div>{{#NAVCONTENT:Answer\|Answer 8.3\|Solution\|Solution 8.3}}
		+
		+
		+	===Exercise 8.4===
		+	<div class="ovning">
		+
		+	A particle has a constant acceleration (<math>0.2\mathbf{i}+0.3\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-2}}</math>. Initially it has a velocity (<math>4\mathbf{i}– 8\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-1}}</math> and is at the point with position vector (<math>6\mathbf{i}+2\mathbf{j}</math>) m.
		+
		+	a) Find the speed of the particle after 10 seconds.
		+
		+	b) Find the position vector of the particle after 10 seconds.
		+
		+	c) When is the velocity of the particle (<math>4.8\mathbf{i}– 6.8\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-1}}</math>?
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 8.4a\|Answer b\|Answer 8.4b\|Answer c\|Answer 8.4c\|Solution a\|Solution 8.4a\|Solution b\|Solution 8.4b\|Solution c\|Solution 8.4c}}

Ian den 12 september 2009 kl. 16.04

2009-09-12T16:04:46Z

← Äldre version		Versionen från 12 september 2009 kl. 16.04
Rad 42:		Rad 42:
	The acceleration of a body is (<math>2\mathbf{i}+3\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-2}}</math>. If the body starts at rest at the origin and accelerates for 4 seconds find the velocity and position of the body at the end of the 4 seconds. The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are perpendicular.		The acceleration of a body is (<math>2\mathbf{i}+3\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-2}}</math>. If the body starts at rest at the origin and accelerates for 4 seconds find the velocity and position of the body at the end of the 4 seconds. The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are perpendicular.

-	~~[[Image:E6.1.GIF]]~~	+
	</div>{{#NAVCONTENT:Answer\|Answer 8.3\|Solution\|Solution 8.3}}		</div>{{#NAVCONTENT:Answer\|Answer 8.3\|Solution\|Solution 8.3}}

Ian den 12 september 2009 kl. 16.01

2009-09-12T16:01:56Z

← Äldre version		Versionen från 12 september 2009 kl. 16.01
Rad 36:		Rad 36:

	</div>{{#NAVCONTENT:Answer\|Answer 8.2\|Solution a\|Solution 8.2a\|Solution b\|Solution 8.2b}}		</div>{{#NAVCONTENT:Answer\|Answer 8.2\|Solution a\|Solution 8.2a\|Solution b\|Solution 8.2b}}
		+
		+	===Exercise 8.3===
		+	<div class="ovning">
		+
		+	The acceleration of a body is (<math>2\mathbf{i}+3\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-2}}</math>. If the body starts at rest at the origin and accelerates for 4 seconds find the velocity and position of the body at the end of the 4 seconds. The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are perpendicular.
		+
		+	[[Image:E6.1.GIF]]
		+	</div>{{#NAVCONTENT:Answer\|Answer 8.3\|Solution\|Solution 8.3}}