Answer:
v_{4}= 80.92[m/s] (Heading south)
Explanation:
In order to calculate this problem, we must use the linear moment conservation principle, which tells us that the linear moment is conserved before and after the collision. In this way, we can propose an equation for the solution of the unknown.
ΣPbefore = ΣPafter
where:
P = linear momentum [kg*m/s]
Let's take the southward movement as negative and the northward movement as positive.
where:
m₁ = mass of car 1 = 14650 [kg]
v₁ = velocity of car 1 = 18 [m/s]
m₂ = mass of car 2 = 3825 [kg]
v₂ = velocity of car 2 = 11 [m/s]
v₃ = velocity of car 1 after the collison = 6 [m/s]
v₄ = velocity of car 2 after the collision [m/s]
![-(14650*18)+(3825*11)=(14650*6)-(3825*v_{4})\\v_{4}=80.92[m/s]](https://tex.z-dn.net/?f=-%2814650%2A18%29%2B%283825%2A11%29%3D%2814650%2A6%29-%283825%2Av_%7B4%7D%29%5C%5Cv_%7B4%7D%3D80.92%5Bm%2Fs%5D)
A mass suspended from a spring is oscillating up and down, (as stated but not indicated).
A). At some point during the oscillation the mass has zero velocity but its acceleration is non-zero (can be either positive or negative). <em>Yes. </em> This statement is true at the top and bottom ends of the motion.
B). At some point during the oscillation the mass has zero velocity and zero acceleration. No. If the mass is bouncing, this is never true. It only happens if the mass is hanging motionless on the spring.
C). At some point during the oscillation the mass has non-zero velocity (can be either positive or negative) but has zero acceleration. <em>Yes.</em> This is true as the bouncing mass passes through the "zero point" ... the point where the upward force of the stretched spring is equal to the weight of the mass. At that instant, the vertical forces on the mass are balanced, and the net vertical force is zero ... so there's no acceleration at that instant, because (as Newton informed us), A = F/m .
D). At all points during the oscillation the mass has non-zero velocity and has nonzero acceleration (either can be positive or negative). No. This can only happen if the mass is hanging lifeless from the spring. If it's bouncing, then It has zero velocity at the top and bottom extremes ... where acceleration is maximum ... and maximum velocity at the center of the swing ... where acceleration is zero.
To find how far east we drove (This is the displacement), we simple subtract 12 from 40.
An easy way to do this in your head is to round 12 down to 10, subtract 10 from 40, then subtract the remaining 2. This should result in an answer showing that you drove 28 miles east.
