Select the correct answer.
What is the momentum of a 76-kilogram horse running at a speed of 45 kilometers/hour?
A. $2.5 \times 10^2$ kilogram-meters/second
B. $3.4 \times 10^4$ kilogram meters/second
C. $3.4 \times 10^3 kilogram$-meters/second
D. $9.5 \times 10^2$ kilogram-meters/second
Answer (1)
Convert the speed from km/hr to m/s: v = 45 hr km = 12.5 s m .
Calculate the momentum using the formula p = m v : p = 76 kg × 12.5 s m = 950 kg ⋅ s m .
Express the momentum in scientific notation: 950 = 9.5 × 1 0 2 .
The momentum of the horse is 9.5 × 1 0 2 kg ⋅ s m .
Explanation
Understanding the Problem We are given the mass of a horse, m = 76 kg, and its speed, v = 45 km/hr. We need to find the momentum of the horse.
Converting Units First, we need to convert the speed from kilometers per hour (km/hr) to meters per second (m/s). To do this, we use the conversion factors: 1 km = 1000 m and 1 hr = 3600 s. Therefore,
v (m/s) = 45 hr km × 1 km 1000 m × 3600 s 1 hr
v (m/s) = 45 × 3600 1000 m/s = 45 × 18 5 m/s = 12.5 m/s
Calculating Momentum Now that we have the speed in m/s, we can calculate the momentum p using the formula:
p = m v
where m is the mass and v is the velocity. Plugging in the values, we get:
p = 76 kg × 12.5 m/s = 950 kg m/s
Expressing in Scientific Notation We need to express the result in scientific notation to match the given options. 950 can be written as 9.5 × 1 0 2 . Therefore, the momentum of the horse is 9.5 × 1 0 2 kg m/s.
Final Answer Comparing our result with the given options, we find that option D matches our calculated momentum.
Therefore, the correct answer is D. 9.5 × 1 0 2 kilogram-meters/second.
Examples
Understanding momentum is crucial in many real-world applications, especially in physics and engineering. For instance, when designing vehicles, engineers must consider the momentum of the vehicle to ensure safety during collisions. A higher momentum means a greater impact force, which needs to be accounted for in the vehicle's structural design. Similarly, in sports, understanding momentum helps athletes optimize their performance, such as in baseball where the momentum of the bat and ball determines the force of the hit, or in football where the momentum of players affects the outcome of tackles. By calculating and understanding momentum, we can better analyze and predict the outcomes of various physical interactions.
