You will be hiking to a lake with some of your friends by following the trails indicated on a map at the trailhead. the map says that you will travel 4.00 mi directly north, then 5.31 mi in a direction 35.0° east of north, then finally 1.10 mi in a direction 15.0° north of east. assume north to be +y and east to be +x. find the direction of the displacement vector for the hike. enter the answer as an angle north of east.

You are in a car that is traveling along highway 99 at a constant speed of 16 m/s. suddenly you see a truck also traveling at a constant speed (3.0 m/s) that is on a track to cross your lane from an alley on the right and is moving into your lane (which you can’t get out of, because of broader safety concerns like head on traffic in the other lane). your car’s maximum acceleration is 6.0 m/s2 (either way, gettingfaster or slower) and your reaction time of 0.75 s between first seeing the truck and applying the brake or the accelerator. the distance from the side street, where you first notice the truck, to the right edge of your lane is 2.0 m and the lane also has a fixed width of 4.0m, check for yourself that all these numbers are reasonable. you will assume a reasonable size for your car. the truck is 3.0 m wide.a) how long will it take the truck from the moment you notice it, to block enough of your lane so you can’t slip past while also staying in your own lane (in seconds)? b) how far will your car travel (in meters) while your brain is figuring out what to do? c) if you decide that braking is in your best interests how long will it take you to come to a complete stop once you begin the process of braking (in s)? d) what is the minimum distance (in m) you must be from the truck to successfully stop before hitting