A car (mass = 1140 kg) is traveling at 27.3 m/s when it collides head-on with a sport utility vehicle (mass = 2380 kg) traveling in the opposite direction. In the collision, the two vehicles come to a halt. At what speed was the sport utility vehicle traveling?
I did 1140(27.3) + 2380(v2) / 1140+2380
31122 + 2380v2 / 3520 = speed of Sport utility.
Did I set this up correctly. If so I am stuck on how to solve for v2 now.
original momentum=final momentum
1140*27.3+2380V=(totalmass)*0
V=-1149*27.3/2380
Yes, you have set up the equation correctly. Now, let's solve for v2.
To solve for v2, we need to isolate it on one side of the equation. Let's work step by step:
1. Simplify the equation:
1140(27.3) + 2380(v2) = 31122 + 2380v2
2. Expand the multiplication:
31062 + 2380v2 = 31122 + 2380v2
3. Subtract 2380v2 from both sides:
31062 = 31122
4. At this point, we can see that the equation doesn't have a solution. This means that there might be an error in the earlier calculations or setup of the equation. Let's go over it again:
The conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision.
Initial momentum of car = mass of car * initial velocity of car
Initial momentum of sport utility vehicle = mass of SUV * initial velocity of SUV
Final momentum after collision = 0 since both vehicles come to a halt.
So, we can write the equation as:
(mass of car * initial velocity of car) + (mass of SUV * initial velocity of SUV) = 0
Plugging in the values:
(1140 kg * 27.3 m/s) + (2380 kg * initial velocity of SUV) = 0
31062 + (2380 kg * initial velocity of SUV) = 0
Now, let's solve for the initial velocity of the SUV:
2380 kg * initial velocity of SUV = -31062
Divide both sides by 2380 kg:
initial velocity of SUV = -31062 / 2380 kg
Calculate the result:
initial velocity of SUV = -13.05 m/s
Therefore, the initial velocity of the sport utility vehicle was approximately -13.05 m/s. The negative sign indicates that the SUV was traveling in the opposite direction of the car.