The answers to this problem are: a) mag. of mom.=25.3x10^6 kg-m/s & angle=71.6 d

Question

The answers to this problem are:

a) mag. of mom.=25.3x10^6 kg-m/s & angle=71.6 degrees

b) 8x10^6 N in y direction

c) 800m/s

d) 600 m/s

I just need to see how to get the answers.

Hans Solo is piloting a rocket ship with mass 4.0x10 kg on route to planet Buckeyes is rocket's position as a function of time, is given by N(t (-5.0+2.0t)x10 and y(t 1.0x10tz (with and y in m and t in seconds (neglect gravity and assume the mass of the rocket is constant for this problem) a) 10 pts: What is the magnitude and direction (angle with respect to -x-axis) of the rocket's linear momentum att 3 seconds? b) 10 pts: What is the magnitude and direction ofthe net force acting on the rocket at t-3 seconds? e) 7 pts: Hans Solo steers the rocket so it is now moving in the x direction with constant velocity, 6.0x 0- m/s. Soon after he does this Chewbacca accidently hits the destruct button and the rocket explodes into two pieces, one with ma 1.0x10 kg, the other with m2 -3.0x10 kg. If m is at rest after the explosion what is the speed of m2 after the explosion? d) 3 pts: What is the speed of the rocket's center of mass two seconds after the explosion?

Explanation / Answer

part 1 )

momentum = p = m*v

vx = dx/dt = 2 x 10^3

vy = 2 x 10^3 *t

at t =3 sec

vy = 6 x 10^3

momentum in x direction

px = 8 x 10^6 kg.m/s

py = 2.4 x 10^7 kg.m/s

since momentum is vector quantity

|p| = sqrt(vx^2+vy^2)

|p| = 25.3 x 10^6 kg-m/s

theta = tan^-1(py/px) = 71.6 degree

part b )

a = dv/dt = 2 x 10^3

acceleratuion is constant

F = ma

F = 8 x 10^6 N ( y direction )

part c )

here linear momentum remain conserve

mv = m1v1 + m2v2

since m1 is at rest so v1 = 0

4 x 10^3 * 6 x 10^2 = 0 + 3 x 10^3 * v2

v2 = 800 m/s

part d )

vcm = m1v1+m2v2/(m1+m2)

vcm = (0 + 3 x 10^3 * 800 ) / ( 1x10^3 + 3 x 10^3)

vcm = 600 m/s

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