Question

a plane is ascending at an angle of 9° from the horizontal. the plane’s current altitude is 3.1 km. see the figure below. (the figure is not drawn to scale.) find the plane’s new altitude, h, after 0.10 hours if it travels at a constant speed of 500 km/hr along the direction of its flight. carry your intermediate computations to at least four decimal places, and round your answer to the nearest tenth of a kilometer.

Explanation:

Step1: Calculate distance traveled

The plane's speed is 500 km/hr, and time is 0.10 hours. Using \( \text{distance} = \text{speed} \times \text{time} \), we get \( 500 \times 0.10 = 50 \) km.

Step2: Use sine for altitude gain

In the right triangle, the altitude gain (\( \Delta h \)) from the new distance (50 km) at \( 9^\circ \) is \( \Delta h = 50 \times \sin(9^\circ) \). Calculate \( \sin(9^\circ) \approx 0.1564 \), so \( \Delta h \approx 50 \times 0.1564 = 7.82 \) km.

Step3: Total altitude \( h \)

Add initial altitude (3.1 km) to gain: \( h = 3.1 + 7.82 = 10.92 \), rounded to nearest tenth is 10.9.

Answer:

10.9