A navy destroyer is exactly 68 miles North of an aircraft carrier, which is travelling West 21 degrees North at 18 mph. what speed and bearing must the destroyer maintain if it is to reach the aircraft carrier in exactly 3 hrs?
is it 226mph?
mr.lynch????class
how far do you get? Can you draw a diagram showing the distances?
To find the speed and bearing the destroyer must maintain to reach the aircraft carrier in exactly 3 hours, we will need to break down and solve the problem step by step.
First, let's find the distance the aircraft carrier will travel in 3 hours. We know its speed is 18 mph, so to find the distance, we multiply the speed by the time:
Distance = Speed * Time
Distance = 18 mph * 3 hours
Distance = 54 miles
Next, let's find the direction and distance from the destroyer to the aircraft carrier using the given information. The destroyer is 68 miles north of the aircraft carrier, and the aircraft carrier is traveling west at 21 degrees north.
We can use trigonometry to find the horizontal and vertical components of the distance. The vertical component (north-south distance) is 68 miles, and the horizontal component (east-west distance) can be found using the trigonometric function cosine.
Horizontal Component = Distance * Cosine(Bearing)
Horizontal Component = 54 miles * Cosine(21 degrees)
Horizontal Component ≈ 49.95 miles
Now, let's find the speed the destroyer must maintain. Since the time to reach the aircraft carrier is fixed at 3 hours, we can find the speed by dividing the horizontal component of the distance by the time:
Speed = Horizontal Component / Time
Speed = 49.95 miles / 3 hours
Speed ≈ 16.65 mph
Lastly, let's find the bearing the destroyer must maintain. Since the aircraft carrier is moving west at 21 degrees north, the bearing of the destroyer will be the same. So, the bearing is 21 degrees north.
Therefore, the required speed for the destroyer to reach the aircraft carrier in exactly 3 hours is approximately 16.65 mph, and the bearing it must maintain is 21 degrees north.
Based on the calculations, the statement that the destroyer must maintain a speed of 226 mph is incorrect.