An airplane maintains a speed of 630 km / h relative to the air it is flying through as it makes

step 1 In this exercise, we have an airplane that's heading northward towards a city that's located 750

An airplane maintains a speed of 630 km / h relative to the...

An airplane maintains a speed of 630 $\mathrm{km} / \mathrm{h}$ relative to the air it is flying through as it makes a trip to a city 750 $\mathrm{km}$ away to the north. ( a) What time interval is required for the trip if the plane flies through a headwind blowing at 35.0 $\mathrm{km} / \mathrm{h}$ toward the south? (b) What time interval is required if there is a tailwind with the same speed? (c) What time interval is required if there is a crosswind blowing at 35.0 $\mathrm{km} / \mathrm{h}$ to the east relative to the ground?

Key Concepts

Ground Speed

Ground speed is the speed at which the airplane is moving relative to the ground. It is the resultant of the vector addition of the airplane’s airspeed and the wind velocity. In situations with headwinds, tailwinds, or crosswinds, the ground speed is different from the airspeed, affecting the total travel time.

Time-Distance Relationship

This fundamental concept in kinematics states that the time required for a journey is equal to the distance divided by the speed. In the context of wind effects on airplane travel, determining the effective ground speed using vector addition allows for computing the travel time using the formula time = distance / ground speed.

Relative Velocity

This concept involves understanding how the speed of an object is measured relative to a particular frame of reference. In problems involving aircraft and wind, the airplane's speed relative to the air (its airspeed) must be combined with the wind's velocity relative to the ground to determine the airplane’s actual speed and direction over the ground.

Vector Addition

Vector addition is used to combine different velocity vectors, such as the airplane’s velocity and the wind velocity. This method allows one to determine the resultant ground velocity. The principle involves breaking the velocities into components (for example, north-south and east-west) and then summing these components to achieve the overall velocity vector.

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