Question

С самолета, летящего горизонтально со скоростью 144 км/ч, сбросил пакет с почтой. На какой высоте летел самолет, если за время падения пакет сместился по горизонтальному направлению на 152 м? Сопротивление воздуха не учитывать.

Answer 1

Найдём время падения. Закон движения тела по горизонтальной оси:

S = Vot + gt^2/2

152 = 40t + 4,9t^2

t = 2,94 c.

По вертикальной оси:

h = gt^2/2 = 9,8 * 2,94 * 2,94 / 2 = 42,35 м.

Answer 2

Calculation of the Height of the Plane

To determine the height at which the plane was flying when it dropped the package, we can use the information provided about the horizontal displacement of the package during its fall.

Given: - Horizontal displacement of the package: 152 m - Speed of the plane: 144 km/h

To calculate the height, we need to convert the speed of the plane from km/h to m/s.

Conversion of Speed: 1 km/h = 1000 m / (60 * 60) s = 0.2778 m/s

Therefore, the speed of the plane is: 144 km/h * 0.2778 m/s = 40 m/s

Now, we can use the equations of motion to calculate the height.

Equation of Motion: The horizontal displacement of the package can be calculated using the equation: d = v*t where: - d is the horizontal displacement (152 m), - v is the horizontal velocity of the package (equal to the horizontal velocity of the plane, which is 40 m/s), - t is the time taken for the package to fall.

Since the package is dropped from rest, the initial vertical velocity is 0 m/s. The acceleration due to gravity is approximately 9.8 m/s^2.

Equation of Motion for Vertical Displacement: The vertical displacement of the package can be calculated using the equation: d = (1/2) * g * t^2 where: - d is the vertical displacement (unknown), - g is the acceleration due to gravity (9.8 m/s^2), - t is the time taken for the package to fall.

By equating the two equations, we can solve for t.

Equating the Equations: v*t = (1/2) * g * t^2

Simplifying the equation: 40 m/s * t = (1/2) * 9.8 m/s^2 * t^2

Rearranging the equation: (1/2) * 9.8 m/s^2 * t^2 - 40 m/s * t = 0

Solving this quadratic equation will give us the time taken for the package to fall.

Using the quadratic formula: t = (-b ± √(b^2 - 4ac)) / (2a)

where: a = (1/2) * 9.8 m/s^2 b = -40 m/s c = 0

Simplifying the equation: t = (-(-40) ± √((-40)^2 - 4 * (1/2) * 9.8 * 0)) / (2 * (1/2) * 9.8)

t = (40 ± √(1600)) / 9.8

Calculating the values: t = (40 ± 40) / 9.8

Taking the positive value: t = (40 + 40) / 9.8 = 80 / 9.8 ≈ 8.16 s

Now that we have the time taken for the package to fall, we can calculate the height using the equation of motion for vertical displacement.

Calculating the Height: d = (1/2) * g * t^2

Substituting the values: d = (1/2) * 9.8 m/s^2 * (8.16 s)^2

Calculating the value: d ≈ 0.5 * 9.8 m/s^2 * 66.6256 s^2 ≈ 325.92 m

Therefore, the plane was flying at a height of approximately 325.92 meters when it dropped the package.

Please note that this calculation assumes no air resistance.