Physics, chemistry, engineering and other practical calculations
Problem: An object falls from a height of 100 meters. Calculate its velocity upon impact. (g = 9.8 m/s²)
Formula:v = √(2gh)
Problem: An object is launched at 30° with an initial velocity of 20 m/s. Calculate the horizontal range.
Formula:R = v²sin(2θ)/g
Problem: A circular motion with radius 2 meters and velocity 5 m/s. Calculate the period.
Formula:T = 2πr/v
Problem: Dilute 500 mL of 2M solution to 2L. Calculate the final concentration.
Formula:C₁V₁ = C₂V₂
Problem: Given H⁺ concentration of 0.001 M, calculate the pH value.
Formula:pH = -log[H⁺]
Problem: Three resistors of 100Ω, 200Ω, and 300Ω are connected in parallel. Calculate the total resistance.
Formula:1/R = 1/R₁ + 1/R₂ + 1/R₃
Problem: A simply supported beam with 4m span, center load of 10000N, and section modulus of 0.0001m³. Calculate maximum bending stress.
Formula:σ = FL/(4Z)
Problem: Principal of $10,000, annual interest rate of 5%, calculate the future value after 10 years.
Formula:A = P(1 + r)ⁿ
Problem: Loan of $500,000, annual interest rate 4.9%, term 30 years. Calculate monthly payment.
Formula:M = P[r(1+r)ⁿ]/[(1+r)ⁿ-1]
Problem: Calculate the number of ways to choose 3 people from a group of 10.
Formula:C(n,r) = n!/[r!(n-r)!]