You are driving down a two-lane country road, and a truck in the opposite lane is traveling toward you. Suppose that the speed of light in a vacuum is c = \( 65 \mathrm{~m} / \mathrm{s} \). Determine the speed of the truck relative to you when (a) your speed is \( 25 \mathrm{~m} / \mathrm{s} \) and the truck's speed is \( 35 \mathrm{~m} / \mathrm{s} \) and (b) your speed is \( 5.0 \mathrm{~m} / \mathrm{s} \) and the truck's speed is \( 55 \mathrm{~m} / \mathrm{s} \). The speeds given in parts (a) and (b) 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 toward each other, their relative speed is the sum of their individual speeds. ### Given: - Speed of light \( c = 65 \, \text{m/s} \) (though this value is not relevant for the calculations since we are dealing with speeds much less than \( c \)). - Your speed \( v_1 \) and the truck's speed \( v_2 \) are given in each part. ### (a) Your speed is \( 25 \, \text{m/s} \) and the truck's speed is \( 35 \, \text{m/s} \). 1. **Calculate the relative speed**: \[ v_{\text{relative}} = v_1 + v_2 \] where \( v_1 = 25 \, \text{m/s} \) and \( v_2 = 35 \, \text{m/s} \). 2. **Substituting the values**: \[ v_{\text{relative}} = 25 + 35 \] 3. **Calculate**: \[ v_{\text{relative}} = 60 \, \text{m/s} \] ### (b) Your speed is \( 5.0 \, \text{m/s} \) and the truck's speed is \( 55 \, \text{m/s} \). 1. **Calculate the relative speed**: \[ v_{\text{relative}} = v_1 + v_2 \] where \( v_1 = 5.0 \, \text{m/s} \) and \( v_2 = 55 \, \text{m/s} \). 2. **Substituting the values**: \[ v_{\text{relative}} = 5.0 + 55 \] 3. **Calculate**: \[ v_{\text{relative}} = 60.0 \, \text{m/s} \] ### Summary of Results: - (a) The speed of the truck relative to you is \( 60 \, \text{m/s} \). - (b) The speed of the truck relative to you is \( 60.0 \, \text{m/s} \). In both cases, the relative speed of the truck is the same, \( 60 \, \text{m/s} \).