5. Vou are ditiong down a two lane country road, and a truck in the coposice lane is traveling toward you. Suppose that the speed of light in a vacuum is \( \mathrm{C}=65 \mathrm{~m} / \mathrm{s} \). Determine the speed of the truck relative to you whem (a) your speed is \( 25 \mathrm{~m} / \mathrm{s} \) and the truok's speed is \( 35 \mathrm{~m} / \mathrm{s} \) and (C) your speed is \( 5.0 \mathrm{~m} / \mathrm{s} \) and the trod's speed is \( 55 \mathrm{~m} / \mathrm{s} \). Hepseeds given in parts ( a ) and ( O ) are relative to the ground

To determine the speed of the truck relative to you, we can use the concept of relative velocity. When two objects are moving towards each other, their relative speed is the sum of their individual speeds. ### Given: - Speed of light in a vacuum, \( C = 65 \, \text{m/s} \) (though this value is not relevant for the calculations since we are dealing with speeds much less than the speed of light). - Your speed, \( v_y \). - Truck's speed, \( v_t \). ### (a) Your speed is \( 25 \, \text{m/s} \) and the truck's speed is \( 35 \, \text{m/s} \). 1. **Calculate the relative speed**: \[ v_{relative} = v_y + v_t \] Substituting the values: \[ v_{relative} = 25 \, \text{m/s} + 35 \, \text{m/s} \] ### (b) Your speed is \( 5.0 \, \text{m/s} \) and the truck's speed is \( 55 \, \text{m/s} \). 1. **Calculate the relative speed**: \[ v_{relative} = v_y + v_t \] Substituting the values: \[ v_{relative} = 5.0 \, \text{m/s} + 55 \, \text{m/s} \] Now, let's perform the calculations for both parts. Calculate the value by following steps: - step0: Calculate: \(25+35\) - step1: Add the numbers: \(60\) Calculate or simplify the expression \( 5.0 + 55 \). Calculate the value by following steps: - step0: Calculate: \(5+55\) - step1: Add the numbers: \(60\) ### Results: (a) The relative speed of the truck when your speed is \( 25 \, \text{m/s} \) and the truck's speed is \( 35 \, \text{m/s} \) is: \[ v_{relative} = 60 \, \text{m/s} \] (b) The relative speed of the truck when your speed is \( 5.0 \, \text{m/s} \) and the truck's speed is \( 55 \, \text{m/s} \) is also: \[ v_{relative} = 60 \, \text{m/s} \] In both cases, the speed of the truck relative to you is \( 60 \, \text{m/s} \).