PRELIMINARY STAGE 2024
Contest 40
Chemu SHS: 43 points (Winner)
Our Lady of Mt. Carmel Girls' SHS: 33 points
Manya Krobo SHS: 28 points
Contest 41
Adiembra SHS: 34 points (Winner)
St. Paul's Senior High & Minor Seminary: 24 points
Biakoye Community SHS: 07 points
Contest 42
Swedru Secondary School: 49 points (Winner)
Edinaman SHS: 29 points
Techiman SHS: 23 points
FIRST SET OF QUESTIONS
PREAMBLE
Calculate the speed of a particle whose velocity is given by:
QUESTION 1
$\sqrt8\mathbf{i}+\sqrt{28}\mathbf{j}$
ANSWER: 6 m/s
SOLUTION:
$\text{speed}=\sqrt{(\sqrt8)^2+(\sqrt{28})^2}$
$\text{speed}=\sqrt{8+28}$
$\text{speed}=\sqrt{36}$
$\text{speed}=6\text{ m/s}$
QUESTION 2
$\sqrt{15}\mathbf{i}+\mathbf{j}$
ANSWER: 4 m/s
SOLUTION:
$\text{speed}=\sqrt{(\sqrt{15})^2+1^2}$
$\text{speed}=\sqrt{15+1}$
$\text{speed}=\sqrt{16}$
$\text{speed}=4\text{ m/s}$
QUESTION 3
$\sqrt{19}\mathbf{i}+\sqrt{30}\mathbf{j}$
ANSWER: 7 m/s
SOLUTION:
$\text{speed}=\sqrt{(\sqrt{19})^2+(\sqrt{30})^2}$
$\text{speed}=\sqrt{19+30}$
$\text{speed}=\sqrt{49}$
$\text{speed}=7\text{ m/s}$
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PRACTICE QUESTIONS
1. QUESTION: Calculate the speed of a particle whose velocity is $\sqrt{7}\mathbf{i} + 3\mathbf{j}$ m/s.
ANSWER: 4 m/s
SOLUTION:
$\text{speed} = \sqrt{(\sqrt{7})^2 + 3^2}$
$\text{speed} = \sqrt{7 + 9}$
$\text{speed} = \sqrt{16}$
$\text{speed} = 4\text{ m/s}$
2. QUESTION: Calculate the speed of a particle whose velocity is $\sqrt{11}\mathbf{i} + \sqrt{5}\mathbf{j}$ m/s.
ANSWER: 4 m/s
SOLUTION:
$\text{speed} = \sqrt{(\sqrt{11})^2 + (\sqrt{5})^2}$
$\text{speed} = \sqrt{11 + 5}$
$\text{speed} = \sqrt{16}$
$\text{speed} = 4\text{ m/s}$
3. QUESTION: Calculate the speed of a particle whose velocity is $\sqrt{21}\mathbf{i} + 2\mathbf{j}$ m/s.
ANSWER: 5 m/s
SOLUTION:
$\text{speed} = \sqrt{(\sqrt{21})^2 + 2^2}$
$\text{speed} = \sqrt{21 + 4}$
$\text{speed} = \sqrt{25}$
$\text{speed} = 5\text{ m/s}$
4. QUESTION: Calculate the speed of a particle whose velocity is $\sqrt{17}\mathbf{i} + \sqrt{8}\mathbf{j}$ m/s.
ANSWER: 5 m/s
SOLUTION:
$\text{speed} = \sqrt{(\sqrt{17})^2 + (\sqrt{8})^2}$
$\text{speed} = \sqrt{17 + 8}$
$\text{speed} = \sqrt{25}$
$\text{speed} = 5\text{ m/s}$
5. QUESTION: Calculate the speed of a particle whose velocity is $\sqrt{29}\mathbf{i} + \sqrt{7}\mathbf{j}$ m/s.
ANSWER: 6 m/s
SOLUTION:
$\text{speed} = \sqrt{(\sqrt{29})^2 + (\sqrt{7})^2}$
$\text{speed} = \sqrt{29 + 7}$
$\text{speed} = \sqrt{36}$
$\text{speed} = 6\text{ m/s}$
6. QUESTION: Calculate the speed of a particle whose velocity is $\sqrt{45}\mathbf{i} + 2\mathbf{j}$ m/s.
ANSWER: 7 m/s
SOLUTION:
$\text{speed} = \sqrt{(\sqrt{45})^2 + 2^2}$
$\text{speed} = \sqrt{45 + 4}$
$\text{speed} = \sqrt{49}$
$\text{speed} = 7\text{ m/s}$
7. QUESTION: Calculate the speed of a particle whose velocity is $\sqrt{33}\mathbf{i} + 4\mathbf{j}$ m/s.
ANSWER: 7 m/s
SOLUTION:
$\text{speed} = \sqrt{(\sqrt{33})^2 + 4^2}$
$\text{speed} = \sqrt{33 + 16}$
$\text{speed} = \sqrt{49}$
$\text{speed} = 7\text{ m/s}$
8. QUESTION: Calculate the speed of a particle whose velocity is $\sqrt{55}\mathbf{i} + 3\mathbf{j}$ m/s.
ANSWER: 8 m/s
SOLUTION:
$\text{speed} = \sqrt{(\sqrt{55})^2 + 3^2}$
$\text{speed} = \sqrt{55 + 9}$
$\text{speed} = \sqrt{64}$
$\text{speed} = 8\text{ m/s}$
9. QUESTION: Calculate the speed of a particle whose velocity is $\sqrt{77}\mathbf{i} + 2\mathbf{j}$ m/s.
ANSWER: 9 m/s
SOLUTION:
$\text{speed} = \sqrt{(\sqrt{77})^2 + 2^2}$
$\text{speed} = \sqrt{77 + 4}$
$\text{speed} = \sqrt{81}$
$\text{speed} = 9\text{ m/s}$