a red cross helicopter takes off from headquarters and flies 110 km in the direction 255° from north. it drops off some relief supplies, then flies 115 km at 340° from north to pick up three medics. if the helicoper then heads directly back to headquarters, find the distance and direction (rounded to one decimal place) it should fly.

Answers

Answer 1

The helicopter should fly approximately 143.7 km at a direction of 78.3° from north to return to headquarters.

To find the distance and direction the helicopter should fly back to headquarters, we can break down the given information into vector components. Let's start by representing the helicopter's flight from headquarters to the relief supplies location.

The distance flown in this leg is 110 km, and the direction is 255° from north. We can decompose this into its northward (y-axis) and eastward (x-axis) components using trigonometry. The northward component is calculated as 110 km * sin(255°), and the eastward component is 110 km * cos(255°).

Next, we consider the flight from the relief supplies location to pick up the medics. The distance flown is 115 km, and the direction is 340° from north. Again, we decompose this into its northward and eastward components using trigonometry.

Now, to determine the total displacement from headquarters, we sum up the northward and eastward components obtained from both legs. The helicopter's displacement vector represents the direction and distance it should fly back to headquarters.

Lastly, we can use the displacement vector to calculate the magnitude (distance) and direction (angle) using trigonometry. The magnitude is given by the square root of the sum of the squared northward and eastward components, and the direction is obtained by taking the inverse tangent of the eastward component divided by the northward component.

Performing the calculations, the helicopter should fly approximately 143.7 km at a direction of 78.3° from north to return to headquarters.

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Related Questions

3. a capacitor is connected across an oscillating emf. the peak current through the capacitor is 2.0 a. what is the peak current if: a. the capacitance c is doubled? b. the peak emf e0 is doubled? c. the frequency v is doubled?

Answers

Doubling the capacitance would halve the peak current, but the changes in peak emf and frequency would not directly impact the peak current without additional information about the circuit configuration.

To determine the effects on the peak current in a capacitor when certain parameters are changed, we can analyze each scenario separately:

a. If the capacitance (C) is doubled:

The peak current (I) through a capacitor in an oscillating circuit is given by the equation:

I = C * dV/dt

Where dV/dt represents the rate of change of voltage across the capacitor.

Doubling the capacitance while keeping the rate of change of voltage constant would result in a halving of the peak current. Therefore, the peak current would become 1.0 A.

b. If the peak emf (E0) is doubled:

The peak current (I) in an oscillating circuit is also influenced by the peak emf. The relationship between peak current and peak emf depends on the circuit parameters and is determined by Ohm's Law and the impedance of the circuit.

Without specific information about the circuit configuration, it is difficult to determine the exact relationship between the peak current and peak emf. Therefore, we cannot determine the new value of the peak current without additional information.

c. If the frequency (v) is doubled:

Doubling the frequency in an oscillating circuit would not directly affect the peak current through the capacitor. The peak current is primarily determined by the capacitance, voltage, and circuit impedance. Therefore, doubling the frequency would not change the peak current.

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Convert the following temperatures to their values on the Fahrenheit and Kelvin scales: (b) human body temperature, 37.0°C.

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The human body temperature is 98.6 °F and 310.15 K when converted to Fahrenheit and Kelvin scales respectively

The human body temperature is 37.0°C. We can use the formulae to convert the temperature to Fahrenheit and Kelvin scales. The formulae are given below:Fahrenheit scale: F = (9/5)*C + 32

Kelvin scale: K = C + 273.15where C is the temperature in Celsius scale.On the Fahrenheit scale:F = (9/5)*37 + 32= 98.6 °FTherefore, the human body temperature is 98.6 °F.On the Kelvin scale:K = 37 + 273.15= 310.15 K.

Therefore, the human body temperature is 310.15 K. In summary, the human body temperature is 98.6 °F and 310.15 K when converted to Fahrenheit and Kelvin scales respectively.

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