Final answer:
The student's question involves solving a quadratic equation using the provided constants and understanding dimensional consistency in equations. Additionally, the concept of exponential growth is discussed in the context of calculating size increase over a period of time.
Step-by-step explanation:
Solving Quadratic Equations and Dimensional Analysis
Based on the provided information, the expression in question is a quadratic equation that can be solved using the quadratic formula. Given the constants a=4.90, b=-14.3, and c=-20.0, we can solve for t using the equation at² + bt + c = 0. The dimensions for each term are also given, confirming that the equation is dimensionally consistent. For linear equations, dimensional analysis helps determine the unit measurements for physical quantities. The change in height mentioned for Block B reveals a proportional relationship to Block A, indicating a linear relationship.
Exponential growth models can be used to calculate growth over time, such as a 63% increase in size over 10 years using Equation 1.1 or 1.2 with specified values. The growth rate or base and the number of steps or time can vary but produce the same result due to the properties of exponential functions.
To solve the quadratic equation given, we use the quadratic formula: t = (-b ± √(b² - 4ac))/(2a). After calculating the discriminant (b² - 4ac) and applying it to the formula, we find the values of t that satisfy the equation.