8. Exercises
From Mechanics
| Line 58: | Line 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}} | ||
Revision as of 16:29, 12 September 2009
| Theory | Exercises |
Exercise 8.1
The acceleration of a jet-ski is (\displaystyle 0.9\mathbf{i}+0.7\mathbf{j}) \displaystyle \text{m}{{\text{s}}^{-2}}. Its initial velocity is 4\displaystyle \mathbf{i} \displaystyle \text{m}{{\text{s}}^{-1}} and its initial position is (\displaystyle 400\mathbf{i}+350\mathbf{j}) m. The unit vectors are directed east and north respectively.
a) Find the velocity of the jet-ski when t = 10 seconds.
b) Find the position of the jet-ski when t = 10 seconds.
Loading...
Exercise 8.2
A particle is set into motion on a smooth inclined plane. The initial velocity of the particle is 5\displaystyle \mathbf{i} \displaystyle \text{m}{{\text{s}}^{-1}}, its acceleration is -4\displaystyle \mathbf{j} \displaystyle \text{m}{{\text{s}}^{-2}} and its initial position is (\displaystyle 18\mathbf{i}+14\mathbf{j}) m, where \displaystyle \mathbf{i} and \displaystyle \mathbf{j} are perpendicular unit vectors that lie in the plane in which the particle is moving.
a) Find the velocity of the particle after it has been moving for 4 seconds.
b) Find the position of the particle after it has been moving for 8 seconds.
Exercise 8.3
The acceleration of a body is (\displaystyle 2\mathbf{i}+3\mathbf{j}) \displaystyle \text{m}{{\text{s}}^{-2}}. 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 \displaystyle \mathbf{i} and \displaystyle \mathbf{j} are perpendicular.
Exercise 8.4
A particle has a constant acceleration (\displaystyle 0.2\mathbf{i}+0.3\mathbf{j}) \displaystyle \text{m}{{\text{s}}^{-2}}. Initially it has a velocity (\displaystyle 4\mathbf{i}– 8\mathbf{j}) \displaystyle \text{m}{{\text{s}}^{-1}} and is at the point with position vector (\displaystyle 6\mathbf{i}+2\mathbf{j}) 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 (\displaystyle 4.8\mathbf{i}– 6.8\mathbf{j}) \displaystyle \text{m}{{\text{s}}^{-1}}?
Exercise 8.5
A light aeroplane has a velocity of 80\displaystyle \mathbf{i} \displaystyle \text{m}{{\text{s}}^{-1}}, as it is moving along a runway. When it takes off it then experiences an acceleration of (\displaystyle \mathbf{i}+4\mathbf{j}) \displaystyle \text{m}{{\text{s}}^{-2}} for the first 30 seconds of its flight. The unit vectors \displaystyle \mathbf{i} and \displaystyle \mathbf{j} 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.
