Question

A plane flies 1.5 hours at 120 mph on a bearing of 10 degrees. It then turns and flies 8.5 hours at the same speed on a bearing of 100 degrees. How far is the plane from its starting​ point

Answer 1

Answer:

Plane is 1035.76 miles far away from the starting point.

Explanation:

 First the plane flies 1.5 hours at 120 mph on a bearing of 10 degrees then it turns and flies 8.5 hours at the same speed on a bearing of 100 degrees.

 So angle between the displacements = 100-10 = 90 degrees

 Initial displacement = 1.5 *120 = 180 miles

 Second displacement = 8.5*120 = 1020 miles

These two displacements are at 90 degrees, so final displacement = $\sqrt{180^2+1020^2} = 1035.76miles$

So plane is 1035.76 miles far away from the starting point.

Answer 2

The distance of the plane from its starting point is 1,035.8 miles.

The given parameters;

• initial time of motion, t = 1.5 hours
• speed of the motion, = 120 mph
• final time of motion, t= 8.5 hours
• final speed = 120 mph

The initial displacement of the plane is calculated as follows;

$x_1 = 1.5 \times 120 \\\\x_1 = 180 \ miles$

The final displacement of the plane is calculated as follows;

$x_2 = 8.5 \times 120\\\\x_2 = 1020\ miles$

The angle between the initial displacement and final displacement;

$\theta = 100^0 - 10 ^0 = 90^0$

The distance of the plane from its starting point is calculated as follows;

$d^2 = x_1^2 + x_2^2\\\\d = \sqrt{180^2 + 1020^2} \\\\d = 1,035.8 \ miles$

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