How fast would a 9-g fly have to be traveling to slow a 1910-kg car traveling at 61 mph by 6 mph if the fly hit the car in a totally inelastic head-on collision?
Could someone explain the steps, please?
The answer is supposed to be 1.27e+06 mph, but I'm not sure how to solve for it.
Use conservation of momentum for inelastic collisions (when both masses travel at the same final speed in the same direction):
m1u1+m2u2=(m1+m2)v
Here
m1=0.009 kg
u1=to be found
m2=1910 kg
u2=61 mph
(m1+m2)=1910.009
v2=55 mph
So
0.009u1+1910*61 = (1910.009)(55)
Solve for u1
u1=(1910.009*55-1910*61)/0.009
=-1.27*106 m/s
The negative sign means the fly travels in the opposite direction to the car.
it wouldn't slow the car down at all its redundet there just isn't enough pressure behind the fly to stop the car or to slow it down it would kill the fly and make a speck of guts on the windshield
To solve this problem, you need to apply the principles of conservation of momentum. Here's how you can solve it step by step:
1. Determine the initial momentum of the car:
- The initial momentum (p1) of an object is the product of its mass (m) and velocity (v).
- Given that the mass of the car (m1) is 1910 kg and its initial velocity (v1) is 61 mph, we need to convert the velocity to meters per second (m/s). 1 mph = 0.44704 m/s.
- So, the initial momentum of the car (p1) can be calculated as follows: p1 = m1 * v1.
2. Determine the final momentum of the car:
- After the fly hits the car, their velocities become the same due to the totally inelastic collision.
- Let's assume the final velocity (v2) of both the fly and the car after the collision is v.
- The mass of the fly (m2) is given as 9 g, which we need to convert to kg (9 g = 0.009 kg).
- The momentum (p2) of both objects after the collision is equal to their combined mass times the final velocity (p2 = (m1 + m2) * v2).
3. Apply the conservation of momentum principle:
- According to the conservation of momentum, the total momentum of the system before the collision (p1) should be equal to the total momentum after the collision (p2).
- Therefore, we can set up the equation p1 = p2 and solve for the final velocity (v2).
4. Calculate the change in velocity of the car:
- The change in velocity (Δv) of the car can be determined by subtracting the final velocity (v2) from the initial velocity (v1). So, Δv = v1 - v2.
5. Plug in the values and solve the equation:
- Substitute the given values into the equation p1 = p2 and solve for v2:
m1 * v1 = (m1 + m2) * v2
- Once you have the value of v2, substitute it into the equation Δv = v1 - v2 to find the change in velocity of the car.
Using these steps, you should be able to calculate the final velocity and the change in velocity of the car after the fly hits it.