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Fundamentals Of Physics
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Short Answer

An object is tracked by a radar station and determined to have a position vector given byr=(3500-160t)i^+2700j^+300k^ ,with rin meters and t in seconds. The radar station’s x axis points east, its y axis north, and its z axis vertically up. If the object is a 250 kg meteorological missile, what are (a) its linear momentum, (b) its direction of motion, and (c) the net force on it?

a) The linear momentum of an object is -4.0×104 kg.msi^.

b) The direction of motion of the object is along the negative x-axis.

c) The net force on the object is 0.

See the step by step solution

Step by Step Solution

Step 1: Listing the given quantities

The mass of an object is,m=250 kg.

The position vector of the object, r=3500-160ti^+2700j^+300k^.

Step 2: Understanding the concept of the law of conservation of momentum

Here, we can apply the calculus knowledge along with Newton’s second law of motion.



Step 3: (a) Calculation of linear momentum

The equation for velocity is,


Substitute the values in the above expression, and we get,

v=d3500-160ti^+2700j^+300k^dt =-160i^

Linear momentum can be calculated as,


Substitute the values in the above expression, and we get,

P=250×-160i^ =-4.0×104 kg.ms

Thus, the linear momentum of an object, P=-4.0×104 kg.ms.

Step 4: (b) Direction of motion

From the equation of velocity, we can say that the direction of motion of the object is (- x) direction.

Thus, the direction of motion is in the -x (west) direction .

Step 5: (c) Calculation of net force

The equation of force in terms of momentum is,


From part a, since the value of P does not change with time, we get,


Thus, the net force on the object, F=0

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