How fast would a 4-g fly have to be traveling to slow a 1890-kg car traveling at 51 mph by 6 mph if the fly hit the car in a totally inelastic head-on collision?
To calculate the speed at which the fly would have to be traveling to slow down the car, we can use the principle of conservation of momentum.
The momentum of an object is defined as the product of its mass and velocity. In a head-on collision, the total momentum before the collision is equal to the total momentum after the collision.
Let's denote the mass of the fly as m and its initial velocity as v. The mass of the car is given as 1890 kg, and its initial velocity is 51 mph. After the collision, the car's velocity decreases by 6 mph.
Using the principle of conservation of momentum, we can set up the following equation:
(m * v) + (1890 kg * 51 mph) = (1890 kg * (51 mph - 6 mph))
Now, we need to convert the masses and velocities to consistent units. Converting the fly's mass to kg (1 kg = 1000 g), and converting mph to m/s (1 mph = 0.447 m/s), the equation becomes:
(m * v) + (1890 kg * 51 * 0.447 m/s) = (1890 kg * (51 - 6) * 0.447 m/s)
Simplifying the equation, we have:
(m * v) + (1890 kg * 22.797 m/s) = (1890 kg * 45 * 0.447 m/s)
Dividing both sides of the equation by (1890 kg), we get:
(m * v) + (22.797 m/s) = (45 * 0.447 m/s)
Subtracting (22.797 m/s) from both sides, we have:
m * v = (45 * 0.447 m/s) - (22.797 m/s)
Calculating the right side of the equation, we get:
m * v = 20.115 m/s
Finally, to find the speed at which the fly must be traveling, we can divide both sides of the equation by the mass of the fly (4 g = 0.004 kg):
v = 20.115 m/s / 0.004 kg
Calculating this yields the speed of the fly as:
v = 5028.75 m/s
So, the 4-g fly would need to be traveling at approximately 5028.75 meters per second to slow down the 1890-kg car by 6 mph in a totally inelastic collision.