While driving in your pickup truck down Highway 280 between San Franscisco and Palo Alto, a meteorite lands in your truck bed! Despite its 220 kg mass, the meteor does not destroy your 1200 kg truck. In fact, it landed so softly it added mass but did not change the total momentum of your truck. Before the meteor landed you were going 25 m/s. After it landed, approximately how fast were you going?
a
21 m/s
b
28 m/s
c
15 m/s
d
32 m/s
a. 21 m/s
To solve this problem, we can use the principle of conservation of momentum. Before the meteorite landed, the total momentum of the truck and the meteorite was equal to the momentum of the truck after the meteorite landed.
The momentum (p) of an object is the product of its mass (m) and velocity (v).
Before the meteorite landed:
Initial momentum of the truck = mass of the truck * velocity of the truck
= 1200 kg * 25 m/s
After the meteorite landed:
Final momentum of the truck and the meteorite = (mass of the truck + mass of the meteorite) * velocity of the truck after the meteorite landed
Since the total momentum of the truck and the meteorite did not change, we can write the equation:
Initial momentum of the truck = Final momentum of the truck and the meteorite
1200 kg * 25 m/s = (1200 kg + 220 kg) * v
Simplifying the equation, we have:
30000 kg m/s = 1420 kg * v
v = 30000 kg m/s / 1420 kg
v ≈ 21.13 m/s
Therefore, approximately, the truck would be going 21 m/s after the meteorite landed.
So, the answer is (a) 21 m/s.