A marine research team is testing two deep-sea probes, Alpha and Beta, by deploying them into a vertical shaft within an underwater trench. Both probes are released from rest at the water's surface.
The acceleration, in m s−2\text{m s}^{-2}m s−2, of each probe is modeled as a function of time, ttt seconds, after release:
Acceleration of Alpha=0.048t2 \text{Acceleration of Alpha} = 0.048t^2 Acceleration of Alpha=0.048t2 Acceleration of Beta=0.016t3 \text{Acceleration of Beta} = 0.016t^3 Acceleration of Beta=0.016t3Determine the time taken for probe Alpha to reach a depth of 150 metres. Give your answer to four significant figures.
The team will select the probe that reaches the 150-metre depth mark in the shortest time. Determine which probe should be selected.
The models assume that both probes respond and accelerate instantaneously at t=0t = 0t=0. In light of this, explain why the team's selection might be incorrect in practice.
