For this case we have the following expressions:
and
Let:
(Integer m)
(Integer n)
By definition, an integer m is divisible by an integer n if the remainder of the division is 0. That is, there is an integer p such that:
Rewriting the expression we have:
So:
We cancel similar terms:
We check:
Answer:
If they are divisible
The final velocity is 15.8 m/s in the forward direction
Step-by-step explanation:
An inelastic collision occurs when the two object after the collision stick together.
In any case, the total momentum of the system is conserved before and after the collision, in absence of external forces. Therefore, we can write:
where in this problem:
m = 1300 kg is the mass of the small sedan
u = 20 m/s is the initial velocity of the small sedan
M = 7100 kg is the mass of the truck
U = 15 m/s is the initial velocity of the truck
v is the final combined velocity of the small sedan + truck
Here we have taken both the velocity of the sedan and the truck in the positive (forward) direction
Solving the equation for v, we find the final velocity:
And since the sign is positive, this means that is direction is the same as the initial direction of the sedan and the truck, so forward.
Learn more about collisions:
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