Question One 23 marks i. What is the importance of measurement in science up Atthrology? (2 marks) b. Check if the equation. v^2=v^2+2as is Specificiently correct where v , 4, A, and S are final velocity, initial velocity, acceleration and displacementrespectively. (3 marks) c. Two forces of magnitude QV and ION are ingined at an angle of 60^circ with each other. Calculate the magnitude of resultant made by resultant with 6N force. (2 marks) 4. List two applications of viscosity. (2 marks) Q A Tiger is crouched 20 m to east of an observer. At time t=0 the Tiger begins to run due east towant an Giraffe that is 50 m to the east of the obscriber, During the first 2.0 seconds of

**Question One**<br /><br />2. **Importance of Measurement in Science and Technology (2 marks)**<br /><br />Measurement is crucial in science and technology for several reasons:<br /><br />- **Precision and Accuracy:** Measurements allow scientists and engineers to obtain precise and accurate data, which is essential for experiments, research, and development. This ensures that results are reliable and can be replicated.<br /><br />- **Standardization:** Measurements provide a standardized way to quantify observations, enabling consistent communication and comparison of data across different studies and technological applications.<br /><br />b. **Dimensional Analysis of the Equation \( v^2 = v_0^2 + 2as \) (3 marks)**<br /><br />To check if the equation is dimensionally correct, we need to analyze the dimensions of each term:<br /><br />- \( v^2 \): The dimension of velocity \( v \) is \([L][T]^{-1}\), so \( v^2 \) has the dimension \([L^2][T]^{-2}\).<br /><br />- \( v_0^2 \): Similarly, the initial velocity \( v_0 \) also has the dimension \([L^2][T]^{-2}\).<br /><br />- \( 2as \): Acceleration \( a \) has the dimension \([L][T]^{-2}\), and displacement \( s \) has the dimension \([L]\). Therefore, \( as \) has the dimension \([L^2][T]^{-2}\).<br /><br />Since all terms have the same dimension \([L^2][T]^{-2}\), the equation is dimensionally correct.<br /><br />c. **Resultant Force Calculation (2 marks)**<br /><br />Given two forces: \( Q = 6 \, \text{N} \) and \( I = 10 \, \text{N} \), inclined at an angle of \( 60^\circ \):<br /><br />The magnitude of the resultant force \( R \) can be calculated using the formula:<br />\[ R = \sqrt{Q^2 + I^2 + 2QI \cos \theta} \]<br /><br />Substitute the given values:<br />\[ R = \sqrt{6^2 + 10^2 + 2 \times 6 \times 10 \times \cos 60^\circ} \]<br />\[ R = \sqrt{36 + 100 + 120 \times 0.5} \]<br />\[ R = \sqrt{36 + 100 + 60} \]<br />\[ R = \sqrt{196} \]<br />\[ R = 14 \, \text{N} \]<br /><br />d. **Applications of Viscosity (2 marks)**<br /><br />Two applications of viscosity are:<br /><br />1. **Lubrication:** Viscosity is a critical property in selecting lubricants for machinery. It determines how well the lubricant can reduce friction between moving parts.<br /><br />2. **Fluid Dynamics:** In fluid dynamics, viscosity affects the flow rate and behavior of fluids in pipes and channels, influencing engineering designs in fields like hydraulics and aerodynamics.<br /><br />e. **Tiger's Motion Problem (Incomplete Question)**<br /><br />The question seems incomplete. Please provide additional details or clarify the scenario for further assistance.