How fast would a 9-g fly have to be traveling to slow a 1790-kg car traveling at 58 mph by 4 mph if the fly hit the car in a totally inelastic head-on collision?
Then the car's initial velocity is -50 mph.
The collision is totally inelastic, so the final velocity of both fly and car is -44 mph.
Total initial momentum = (4/1000)u - 1980*50 = 0.004u - 99000 kg mph.
Total final momentum = (1980 + 4/1000)*(-44) = -87120.176 kg mph.
Momentum is conserved, so 0.004u - 99000 = -87120.176.
�ˆ 0.004u = 99000 - 87120.176 = 11879.824.
�ˆ u = 11879.824/0.004 = 2969956 mph.
So the fly's velocity would have to be 2,969,956 mph. That's almost 825 miles per second!
Just plug in your numbers and chug away.
How are you getting -44 mph for the final velocity?
To determine the speed that a 9-g fly would have to be traveling in order to slow down a 1790-kg car by 4 mph in a totally inelastic head-on collision, we can use the principle of conservation of momentum. The formula for momentum is p = m*v, where p is the momentum, m is the mass, and v is the velocity.
First, let's convert the given measurements to SI units for consistency.
The mass of the fly can be converted from grams (g) to kilograms (kg) by dividing by 1000. So, 9 grams is equal to 0.009 kg.
The speed of the car can be converted from miles per hour (mph) to meters per second (m/s) by multiplying by a conversion factor of 0.447. So, 58 mph is equal to (58 * 0.447) m/s.
The change in velocity (Δv) of the car can also be converted from mph to m/s using the same conversion factor. So, 4 mph is equal to (4 * 0.447) m/s.
Now, let's calculate the initial momentum of the car before the collision. The car's mass (m1) is 1790 kg, and its initial velocity (v1) is (58 * 0.447) m/s. Therefore, the initial momentum (p1) of the car is calculated as:
p1 = m1 * v1
Next, let's calculate the final momentum of the car after the collision. The final velocity (v2) of the car would be equal to its initial velocity (v1) minus the change in velocity (Δv). Therefore, the final momentum (p2) of the car is calculated as:
p2 = m1 * v2
Since the collision is totally inelastic, the two objects stick together and move with the same final velocity. Therefore, the final velocity (v2) of the car is also the final velocity of the fly (v3).
Now, let's calculate the momentum of the fly. The mass (m3) of the fly is 0.009 kg, and its final velocity (v3) is the same as the final velocity of the car (v2). Therefore, the momentum (p3) of the fly is calculated as:
p3 = m3 * v3
According to the principle of conservation of momentum, the total momentum before the collision (p1) should be equal to the total momentum after the collision (p2 + p3).
Therefore, we can set up the equation:
p1 = p2 + p3
Solving for v2, we can rearrange the equation as:
v2 = (p1 - p3) / m1
Substituting the known values into the equation, we can calculate the final velocity (v2) of the car (and the fly):
v2 = (p1 - p3) / m1
Now, we have all the necessary information to solve the problem. Simply substitute the known values into the equation, and calculate v2 to find the speed required for the 9-g fly to slow down the 1790-kg car.