perseus the penguin can fly at a maxium speed of 150 km/hr when there is no wind. Perseus decides to make a trip from hershey to new york to see a broadway play. it is 250 km @ 30 degrees Nof E. if the wind is blowing at 50 km.hr due east, what direction should perseus aim, and how long will the flight last?
To determine the direction Perseus should aim and how long the flight will last, we can break down the problem into components and solve them separately.
First, let's calculate the wind's effect on Perseus' speed. Since the wind is blowing at 50 km/hr due east and Perseus wants to travel northeast, we can break down the wind into its North and East components.
North component of wind = Wind speed × sin(Wind direction angle)
= 50 km/hr × sin(90°) (since due east is 90°)
= 50 km/hr × 1
= 50 km/hr
East component of wind = Wind speed × cos(Wind direction angle)
= 50 km/hr × cos(90°) (since due east is 90°)
= 50 km/hr × 0
= 0 km/hr
Therefore, the wind has no East component, but it has a North component of 50 km/hr.
Next, we can calculate the relative speed and direction of Perseus with respect to the ground.
Relative speed = Maximum speed of Perseus - North component of wind
= 150 km/hr - 50 km/hr
= 100 km/hr
Relative direction = Direction of Perseus + Wind direction angle
= 30° North of East + 0° (due east)
= 30° North of East
So, Perseus should aim 30° North of East and travel at a relative speed of 100 km/hr.
Finally, we can calculate the flight duration using the formula:
Flight duration = Distance / Speed
Given that the distance is 250 km and the relative speed is 100 km/hr:
Flight duration = 250 km / 100 km/hr
= 2.5 hours
Therefore, the flight will last for 2.5 hours.