Two vehicles are approaching an intersection. One is a 2500 kgkg pickup traveling at 14.0 m/sm/s from east to west (the −x−𝑥 -direction), and the other is a 1600 kgkg sedan going from south to north (the +y+𝑦-direction) at 25.0 m/sm/s.Part APart completeFind the x𝑥-component of the net momentum of this system.Express your answer in kilogram meters per second.px𝑝𝑥 =−3.5×104 kg⋅m/skg⋅m/sSubmitPrevious Answers CorrectPart BPart completeFind the y𝑦-component of the net momentum of this system.Express your answer in kilogram meters per second.py𝑝𝑦 =4.0×104 kg⋅m/skg⋅m/sSubmitPrevious Answers CorrectPart CWhat is the magnitude of the net momentum?Express your answer in kilogram meters per second.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typep𝑝 =nothingkg⋅m/skg⋅m/sSubmitRequest AnswerPart DWhat is the direction of the net momentum?Express your answer in degrees measured from north to west.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeθ𝜃
Question
Two vehicles are approaching an intersection. One is a 2500 kgkg pickup traveling at 14.0 m/sm/s from east to west (the −x−𝑥 -direction), and the other is a 1600 kgkg sedan going from south to north (the +y+𝑦-direction) at 25.0 m/sm/s.Part APart completeFind the x𝑥-component of the net momentum of this system.Express your answer in kilogram meters per second.px𝑝𝑥 =−3.5×104 kg⋅m/skg⋅m/sSubmitPrevious Answers CorrectPart BPart completeFind the y𝑦-component of the net momentum of this system.Express your answer in kilogram meters per second.py𝑝𝑦 =4.0×104 kg⋅m/skg⋅m/sSubmitPrevious Answers CorrectPart CWhat is the magnitude of the net momentum?Express your answer in kilogram meters per second.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typep𝑝 =nothingkg⋅m/skg⋅m/sSubmitRequest AnswerPart DWhat is the direction of the net momentum?Express your answer in degrees measured from north to west.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeθ𝜃
Solution
Part A The x-component of the net momentum of the system can be found by multiplying the mass of the pickup by its velocity. Since the pickup is traveling in the negative x-direction, we have:
px = mass_pickup * velocity_pickup px = 2500 kg * 14.0 m/s px = -35000 kg*m/s
Part B The y-component of the net momentum of the system can be found by multiplying the mass of the sedan by its velocity. Since the sedan is traveling in the positive y-direction, we have:
py = mass_sedan * velocity_sedan py = 1600 kg * 25.0 m/s py = 40000 kg*m/s
Part C The magnitude of the net momentum can be found by taking the square root of the sum of the squares of the x and y components of the momentum. This is given by the Pythagorean theorem:
p = sqrt(px^2 + py^2) p = sqrt((-35000 kgm/s)^2 + (40000 kgm/s)^2) p = sqrt(1225000000 + 1600000000) p = sqrt(2825000000) p = 53166.24 kg*m/s
Part D The direction of the net momentum can be found by taking the arctangent of the ratio of the y-component to the x-component of the momentum. This is given by the formula:
θ = arctan(py/px) θ = arctan(40000/-35000) θ = -48.37 degrees
Since the angle is measured from north to west, we add 180 degrees to get the final answer:
θ = -48.37 + 180 θ = 131.63 degrees
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