select the correct answer.\nkelly is driving a car with a mass of 800 kilograms in a south direction with a…

Explanation:

Step1: Calculate car's momentum

The momentum formula is $p = mv$. For the car, $m_{car}=800\ kg$ and $v_{car}=18\ m/s$ in the south - direction. So $p_{car}=m_{car}v_{car}=800\times18 = 14400\ kg\cdot m/s$ (south - direction).

Step2: Calculate truck's momentum

For the truck, $m_{truck}=1500\ kg$ and $v_{truck}=15\ m/s$ in the east - direction. So $p_{truck}=m_{truck}v_{truck}=1500\times15=22500\ kg\cdot m/s$ (east - direction).

Step3: Use vector addition for momentum

Since the two momenta are perpendicular (south and east), we use the Pythagorean theorem for vectors. The magnitude of the total initial momentum $p=\sqrt{p_{car}^{2}+p_{truck}^{2}}$. $p_{car}^{2}=(14400)^{2}=207360000$ and $p_{truck}^{2}=(22500)^{2}=506250000$. $p=\sqrt{207360000 + 506250000}=\sqrt{713610000}\approx 26713\approx2.7\times 10^{4}\ kg\cdot m/s$. In a perfectly inelastic collision, the total momentum is conserved. So the magnitude of the final momentum is the same as the magnitude of the total initial momentum.

Answer:

D. $2.7\times 10^{4}$ kilogram meters/second