Although it cannot sustain its top speed for more than 8.65 s, the cheetah can run a distance of 274 m during that time. If a cheetah with a mass of 50.0 kg is moving at top speed, what is its momentum?

Answer 1

To calculate the momentum of the cheetah when it is moving at its top speed, we can use the formula for momentum:

\[ \text{Momentum} (p) = \text{mass} (m) \times \text{velocity} (v) \]

First, we need to determine the cheetah's velocity while it is running at its top speed. We can do this using the distance it covers and the time it takes to cover that distance.

Given:

• Distance \( d = 274 , \text{m} \)
• Time \( t = 8.65 , \text{s} \)

We can calculate the velocity \( v \) using the formula:

\[ v = \frac{d}{t} \]

Substituting the values:

\[ v = \frac{274 , \text{m}}{8.65 , \text{s}} \approx 31.66 , \text{m/s} \]

Now that we have the velocity, we can calculate the momentum using the mass of the cheetah, which is given as 50.0 kg:

\[ p = m \times v = 50.0 , \text{kg} \times 31.66 , \text{m/s} \]

Calculating the momentum:

\[ p \approx 1583 , \text{kg} \cdot \text{m/s} \]

Therefore, the momentum of the cheetah when it is moving at top speed is approximately 1583 kg·m/s.