Question

Ms Lawrence rode her bike up a hill at 8 miles per hour. She rode her bike down the hill at 16 miles per hour. What is the best prediction of her kinetic energy? KE = ½my*2
(1 point)

She had 2 times the kinetic energy going downhill as she had going uphill.

She had half the kinetic energy going downhill as hse had going uphill.

She had 4 times the kinetic energy going downhill as she had going uphill.

She had the same amount of kinetic energy going uphill and downhill.

Answer 1

To determine Ms. Lawrence's kinetic energy while riding uphill and downhill, we can use the formula for kinetic energy:

\[ KE = \frac{1}{2} mv^2 \]

where \( m \) is mass and \( v \) is velocity.

1. **Kinetic Energy Going Uphill:**
- Speed = 8 mph
\[ KE_{\text{uphill}} = \frac{1}{2} m (8^2) = \frac{1}{2} m (64) = 32m \]

2. **Kinetic Energy Going Downhill:**
- Speed = 16 mph
\[ KE_{\text{downhill}} = \frac{1}{2} m (16^2) = \frac{1}{2} m (256) = 128m \]

Now we compare the kinetic energies:

- Kinetic energy going downhill: \( 128m \)
- Kinetic energy going uphill: \( 32m \)

To find the ratio of the kinetic energies:
\[ \frac{KE_{\text{downhill}}}{KE_{\text{uphill}}} = \frac{128m}{32m} = \frac{128}{32} = 4 \]

This means she had 4 times the kinetic energy going downhill as she had going uphill.

Therefore, the best prediction of her kinetic energy is:

**She had 4 times the kinetic energy going downhill as she had going uphill.**