Question

Alfredo and Sneha are having an ice skating contest. They skate along a long, straight track, and whoever has gone the farthest from their starting point after 5 seconds wins.

If Alfredo can skate at a velocity of \(v(t) = -3 \sin(at) + 6\) feet per second, and Sneha can skate at a velocity of \(g(t) = 2t + 1\) feet per second, who will win the contest?

Select the correct answer below:
A. Alfredo wins.
B. Sneha wins.
C. They tie.

Answer 1

To determine the winner of the contest, the distance each skater covers needs to be calculated by integrating their velocity functions. Alfredo's distance cannot be determined without the value of 'a' in his velocity function. Sneha is found to cover 30 feet after integrating her velocity function from 0 to 5 seconds.

Step-by-step explanation:

To determine who wins the ice skating contest between Alfredo and Sneha, we need to calculate the distance each skater covers in 5 seconds. The distance a skater covers can be found by integrating their velocity function over the specified time interval.

Alfredo's velocity function is v(t) = -3 sin(at) + 6. To find the distance he covers, we integrate this function from 0 to 5. Unfortunately, we are not given the value of 'a' in the sine function, which is necessary to perform the integration. Without this value, we cannot determine Alfredo's distance.

For Sneha, her velocity function is g(t) = 2t + 1. Integrating this from 0 to 5 seconds gives us:

∫ g(t) dt = ∫ (2t + 1) dt = [t^2 + t] from 0 to 5 = (25 + 5) - (0 + 0) = 30 feet.

Without knowing the value of 'a' for Alfredo's function, we cannot conclude who wins the contest between Alfredo and Sneha.