1) Calculate the angle between the following vectors.
A = 6.1 i + 4.6 j + 6.3 k and B = 8.2 i + 2.3 j - 7.0 k.
2) What should be the spring constant k of a spring designed to bring a 1320 kg car to rest from a speed of 116 km/h so that the occupants undergo a maximum acceleration of 5.0 g?
The Attempt at a Solution
1) For this one I don't know how to approach this so I found the force by multiplying it (6.1*8.2)i + (4.6*2.3)j+(6.3*-7.0)k = 16.5 N and I think I'm approaching this wrong.
2) I converted the speed 116 km/h = 31 m/s and 5.0g=49.05 m/s^2.
than used v^2=vo^2+2a(x-xo) to find the distance. x=(v^2-vo^2)/2a
x=31^2/(2*49.05)=9.7961. Next, used F=-kx=ma so k=ma/x, which is 1320*49.05/9.7961=6609.36 N/m and I don't know why this isn't working.