Select the correct answer.
What is the momentum of a $1.5 \times 10^3$ kilogram van that is moving at a velocity of 32 meters/second?
A. 46.9 kilogram meters/second
B. $47 \times 10^3$ kilogram meters/second
C. $4.85 \times 10^2$ kilogram meters / second
D. $4.85 \times 10^4$ kilogram meters/second
Answer (1)
The problem requires calculating the momentum of a van using the formula p = m v .
Substitute the given mass m = 1.5 × 1 0 3 kg and velocity v = 32 m/s into the formula.
Calculate the momentum: p = ( 1.5 × 1 0 3 ) × 32 = 48000 kg m/s.
Express the result in scientific notation: p = 4.8 × 1 0 4 kg m/s. The closest answer is 4.8 × 1 0 4 kg m/s .
Explanation
Understanding the Problem We are given the mass and velocity of a van and asked to find its momentum. Momentum is a measure of how much 'oomph' an object has when it's moving.
Recalling the Momentum Formula The formula for momentum ( p ) is given by: p = m × v where m is the mass of the object and v is its velocity.
Substituting the Values We are given: Mass, m = 1.5 × 1 0 3 kg = 1500 kg Velocity, v = 32 m/s Now, we substitute these values into the momentum formula: p = ( 1.5 × 1 0 3 kg ) × ( 32 m/s )
Calculating the Momentum Calculating the momentum: p = 1500 kg × 32 m/s = 48000 kg m/s = 4.8 × 1 0 4 kg m/s So, the momentum of the van is 4.8 × 1 0 4 kg m/s .
Selecting the Correct Answer Comparing our calculated value with the given options, we see that option D, 4.85 × 1 0 4 kg m/s , is the closest to our calculated momentum of 4.8 × 1 0 4 kg m/s . Note that there might be a rounding difference.
Final Answer Therefore, the correct answer is D.
Examples
Understanding momentum is crucial in many real-world scenarios, especially in vehicle safety and sports. For instance, when designing cars, engineers consider momentum to estimate the impact force during collisions and design safety features like airbags and crumple zones to minimize injuries. In sports, understanding momentum helps athletes improve their performance, such as in baseball where a batter aims to maximize the momentum of the bat upon hitting the ball to achieve a longer hit. Similarly, in football, a running back's momentum determines how difficult they are to tackle.
