The Ratio of Forces: Cement Floor vs Sand Floor

Calculation Explanation:

Given data:

• Height on Cement Floor (h₁) = 1m
• Time taken on Cement Floor (t₁) = 0.1 seconds
• Height on Sand Floor (h₂) = 9m
• Time taken on Sand Floor (t₂) = 1 second

Using the formula for force:

F = ma = m(v - u) / t = m√2gh / t

Calculating the ratio of forces:

F₁/F₂ = √h₁/h₂ × t₁/t₂

Substituting the values:

√1/9 × 0.1/1 = 1/3 × 1/10 = 1/30 = 3/10 F

Therefore, the ratio of forces between Ram jumping onto a cement floor and a sand floor is 3/10 F.