Final answer:
the speed at which they are moving on the barrel ride is approximately 8.38 meters per second.
Step-by-step explanation:
To calculate the speed at which Eva and Harper are moving in the barrel ride, we use the concept of centripetal acceleration. The centripetal acceleration equation is given by:
\[ a = \frac{v^2}{r} \]
Here, \( a \) is the centripetal acceleration, \( v \) is the tangential speed (or the linear speed along the circle's edge), and \( r \) is the radius of the circle.
The acceleration they experience is given to us as 9.48 m/s², and the radius of the barrel is 7.41 m. We are tasked with finding the speed (\( v \)).
To solve for \( v \), we first rearrange the centripetal acceleration formula to solve for \( v ^2 \):
\[ v^2 = a \cdot r \]
Next, we take the square root of both sides to solve for \( v \):
\[ v = \sqrt{a \cdot r} \]
Plugging the given numbers into the equation:
\[ v = \sqrt{9.48 \, \text{m/s}^2 \cdot 7.41 \, \text{m}} \]
After performing the multiplication under the square root and then taking the square root of the result, we find the speed at which Eva and Harper are moving:
\[ v \approx 8.38 \, \text{m/s} \]
So, the speed at which they are moving on the barrel ride is approximately 8.38 meters per second.