which object would have the most momentum? a. a 500 - pound car moving at 20 miles per hour b. a 200 - pound…

which object would have the most momentum? a. a 500 - pound car moving at 20 miles per hour b. a 200 - pound car moving at 60 miles per hour c. a 100 - pound car moving at 80 miles per hour d. a 50 - pound car moving at 100 miles per hour please select the best answer from the choices provided. o a o b o c o d

which object would have the most momentum? a. a 500 - pound car moving at 20 miles per hour b. a 200 - pound car moving at 60 miles per hour c. a 100 - pound car moving at 80 miles per hour d. a 50 - pound car moving at 100 miles per hour please select the best answer from the choices provided. o a o b o c o d

Answer

Explanation:

Step1: Recall momentum formula

Momentum $p = mv$ (where $m$ is mass and $v$ is velocity). We need to calculate $p$ for each option.

Step2: Calculate momentum for option A

First convert 500 - pound to slugs. 1 slug = 32.2 lb, so $m_A=\frac{500}{32.2}\text{ slugs}$, $v_A = 20\text{ mi/h}$. Convert 20 mi/h to ft/s: 1 mi = 5280 ft, 1 h=3600 s, so $v_A=20\times\frac{5280}{3600}\text{ ft/s}\approx29.33\text{ ft/s}$. Then $p_A=\frac{500}{32.2}\times29.33\approx455.6\text{ slug}\cdot\text{ft/s}$.

Step3: Calculate momentum for option B

$m_B=\frac{200}{32.2}\text{ slugs}$, $v_B = 60\text{ mi/h}=60\times\frac{5280}{3600}\text{ ft/s}=88\text{ ft/s}$. Then $p_B=\frac{200}{32.2}\times88\approx546.6\text{ slug}\cdot\text{ft/s}$.

Step4: Calculate momentum for option C

$m_C=\frac{100}{32.2}\text{ slugs}$, $v_C = 80\text{ mi/h}=80\times\frac{5280}{3600}\text{ ft/s}\approx117.33\text{ ft/s}$. Then $p_C=\frac{100}{32.2}\times117.33\approx364.4\text{ slug}\cdot\text{ft/s}$.

Step5: Calculate momentum for option D

$m_D=\frac{50}{32.2}\text{ slugs}$, $v_D = 100\text{ mi/h}=100\times\frac{5280}{3600}\text{ ft/s}\approx146.67\text{ ft/s}$. Then $p_D=\frac{50}{32.2}\times146.67\approx228.4\text{ slug}\cdot\text{ft/s}$.

Answer:

B. a 200 - pound car moving at 60 miles per hour