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 kilogram-meters/second.
Explanation
Problem Introduction 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.
So, we have:
v = 45 hr km = 45 × 1 km 1000 m × 3600 s 1 hr
v = 45 × 3600 1000 s m = 45 × 18 5 s m = 18 45 × 5 s m = 18 225 s m = 12.5 s m
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 s m = 950 kg ⋅ s m
Final Answer The momentum of the horse is 950 kg m/s. Now, we need to express this in scientific notation. 950 = 9.5 × 1 0 2 . Therefore, the momentum is 9.5 × 1 0 2 kg m/s.
Selecting the Correct Option 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 scenarios, especially in sports and transportation. For instance, when designing safety equipment like helmets or car airbags, engineers need to calculate the momentum involved in collisions to ensure effective protection. In sports, coaches use the concept of momentum to optimize training programs, helping athletes maximize their impact and performance. For example, a baseball bat's momentum upon hitting a ball determines how far the ball will travel, influencing the player's strategy and technique.
