Question:
Two buses of length 60 ft and 40 ft are moving parallel towards each other at speeds 15 ft/s and 10 ft/s respectively. Time taken to pass each other is:
Two buses of length 60 ft and 40 ft are moving parallel towards each other at speeds 15 ft/s and 10 ft/s respectively. Time taken to pass each other is:
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When two bodies move towards each other, always add velocities for relative speed.
Updated On: Jun 20, 2026
- \( \frac{4}{5} \, s \)
- \( 4 \, s \)
- \( 8 \, s \)
- \( 20 \, s \)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding relative motion concept.
When two objects move towards each other, their relative speed increases because both contribute to closing the distance. In such problems, we always convert the motion into an equivalent single-body problem using relative velocity.
Step 2: Identifying total distance to be covered.
For two buses crossing each other completely, the total distance to be covered is equal to the sum of their lengths. This is because both buses must completely pass through each other. Thus total distance = \(60 + 40 = 100\) ft.
Step 3: Understanding relative speed direction.
Since both buses are moving towards each other, their velocities add up. This is a key idea in relative motion where opposite directions are treated as additive magnitudes.
Step 4: Calculating relative speed.
Relative speed = \(15 + 10 = 25\) ft/s. This represents how fast the distance between the two buses decreases.
Step 5: Applying time formula.
Time taken = \( \frac{\text{total distance}}{\text{relative speed}} \). This formula is derived from basic kinematics \( t = \frac{s}{v} \).
Step 6: Substituting values.
\( t = \frac{100}{25} \). This simplifies directly to a clean numerical value without approximation.
Step 7: Final computation.
\( t = 4 \, \text{seconds} \). This is the total time required for both buses to completely cross each other.
When two objects move towards each other, their relative speed increases because both contribute to closing the distance. In such problems, we always convert the motion into an equivalent single-body problem using relative velocity.
Step 2: Identifying total distance to be covered.
For two buses crossing each other completely, the total distance to be covered is equal to the sum of their lengths. This is because both buses must completely pass through each other. Thus total distance = \(60 + 40 = 100\) ft.
Step 3: Understanding relative speed direction.
Since both buses are moving towards each other, their velocities add up. This is a key idea in relative motion where opposite directions are treated as additive magnitudes.
Step 4: Calculating relative speed.
Relative speed = \(15 + 10 = 25\) ft/s. This represents how fast the distance between the two buses decreases.
Step 5: Applying time formula.
Time taken = \( \frac{\text{total distance}}{\text{relative speed}} \). This formula is derived from basic kinematics \( t = \frac{s}{v} \).
Step 6: Substituting values.
\( t = \frac{100}{25} \). This simplifies directly to a clean numerical value without approximation.
Step 7: Final computation.
\( t = 4 \, \text{seconds} \). This is the total time required for both buses to completely cross each other.
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