Final answer:
The time it would take for a peregrine falcon to dive from 1.5 kilometers to a 12-meter tree is approximately 41.2 seconds, calculated by dividing the distance of 1488 meters by the falcon's diving speed of 36.11 meters per second.
Step-by-step explanation:
To calculate the least amount of time it would take for a peregrine falcon to dive from a height of 1.5 kilometers and reach a grouse sitting on top of a 12-meter tree, we have to convert all measurements to the same unit and then use the formula for time, which is time = distance / speed.
First, the total distance the falcon must dive is the height above the ground minus the height of the tree. So, the falcon dives 1.5 kilometers - 0.012 kilometers = 1.488 kilometers. Now, we convert this to meters: 1.488 kilometers = 1488 meters.
The speed of the falcon's dive is given as 130 kilometers per hour. Converting this to meters per second, we get 130 km/h * (1000 m / 1 km) * (1 h / 3600 s) = 36.11 m/s.
Now, we can calculate the time using the formula:
time = distance / speed = 1488 m / 36.11 m/s ≈ 41.2 seconds.
The peregrine falcon would take approximately 41.2 seconds to reach the grouse.