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A car is traveling east at 25 m/s relative to the ground. At the same time, a truck moving in the same direction overtakes the car at 35 m/s relative to the ground, while a motorcycle approaches the car from the opposite direction at 20 m/s.
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a. \(10\ \text{ms}^{-1}\ \text{East}\)
b. \(55\ \text{ms}^{-1}\ \text{West}
| a. | \(v_{\text{T rel C}}\) | \(=v_{\text{T}}-v_{\text{C}}\) |
| \(=35-25\) | ||
| \(=10\ \text{ms}^{-1}\ \text{East}\) |
b. Let East be defined as the positive direction for velocity.
| \(v_{\text{M rel T}}\) | \(=v_{\text{M}}-v_{\text{T}}\) | |
| \(=-20-35\) | ||
| \(=-55\ \text{ms}^{-1}\) | ||
| \(=55\ \text{ms}^{-1}\ \text{West}\) |
A motorbike is travelling to the east at 50 ms\(^{-1}\) when it passes a car travelling west at 60 ms\(^{-1}\).
Calculate the velocity of the motorbike relative to the car. (2 marks)
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\(\text{110 ms}^{-1}\ \text{east}\)
Let east be the positive direction and west be the negative direction.
| \(v_{\text{m rel c}}\) | \(=v_{\text{m}}-v_{\text{c}}\) | |
| \(=50-(-60) \) | ||
| \(=110\ \text{ms}^{-1}\) |
Therefore, the velocity of the motorbike relative to the car is 110 ms\(^{-1}\) east.
Plane A is flying due north at 300 kmh\(^{-1}\) when it measures the velocity of plane B flying due south to be 750 kmh\(^{-1}\).
Calculate the velocity of plane B as measured by the pilots on plane B? (3 marks)
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\(\text{ 450 kmh}^{-1}\ \text{south.} \)
Let north be the positive direction and south be the negative direction.
| \(v_{\text{B rel A}}\) | \(=v_{\text{B}}-\ v_{\text{A}}\) | |
| \(-750\) | \(=v_B-300\) | |
| \(v_B\) | \(=-450\) | |
| \(=450\ \text{kmh}^{-1}\ \text{south} \) |