A mother pushes her son in a stroller at a constant speed of 1.44 m/s. The boy t

Question

A mother pushes her son in a stroller at a constant speed of 1.44 m/s. The boy tosses a 55.8-g tennis ball straight up at 1.25 m/s and catches it. The boy's father sits on a bench and watches. (Assume that the stroller moves in the +x direction and that the +y-axis points upward. Express your answers in vector form.) (a) According to the mother, what are the ball's initial and final momenta? P. 0.0804 kg·m/s Pr = kg m/s (b) According to the father, what are the ball's initial and final momenta? kg m/s Pr = kg m/s (c) According to the mother, is the ball's momentum ever zero? If so, when? If not, why not? O Yes, at the top of its arc O Yes, at the very beginning and end of its flight. O No, because the stroller and ball are moving forward with constant speed No, because the bal is always moving along the y-direction. (d) According to the father, is the ball's momentum ever zero? If so, when? If not, why not? Yes, at the top of its arc. O Yes, at the very beginning and end of its flight. No, because the stroller and ball are moving forward with constant speed No, because the ball is always moving along the y-direction.

Explanation / Answer

a)

The mother is pushes her son and son tosses the ball upward. Thus in the mother’s frame of reference ball will have only y directions velocities and no x directional velocity and so about momenta.

Mass of ball = m= 0.055 kg

Initial velocity of ball along x direction = vix = (0i) m/s

Initial velocity of ball along y direction = viy = (1.25j) m/s

Initial momentum along x axis = pix = m*vix = (0i) kg*m/s

Initial momentum along y axis = piy = m*viy= 0.055kg*(1.25 j) kg*m/s =( 0.06875 j) kg*m/s

Initial momentum = Pi = pix + piy = [(0i)+(0.06875j)] kg*m^2

Final velocity of ball along x direction = vfx = (0i) m/s

Final velocity of ball along y direction = vfy = (-1.25j) m/s

Final momentum along x axis = pfx = m*vfx = (0i) kg*m/s

Final momentum = pfy = m*vf = 0.055kg*(-1.25 j) kg*m/s = (-0.06875 j) kg*m/s

Initial momentum = Pf = pfx + pfy = [(0i)+(-0.06875j)] kg*m^2

b)

The boy is moving along x direction which tosses the ball along y direction. Father watches this while sitting on the bench. Thus father will see the ball is moving in both direction in x axis and in y axis also.

So according to the father ball’s initial velocity along x axis = vix = 1.44m/s

So according to the father ball’s initial momentum along x axis =pix=m*vix =0.055kg*1.44m/s = 0.0792kg*m/s

So according to the father ball’s initial velocity along y axis = viy = 1.25m/s

So according to the father ball’s initial momentum along y axis =piy=m*viy =0.055kg*1.25m/s = 0.06875kg*m/s

Total initial momentum = pi = pix + piy = [(0.0792i)+(0.06875j)] kg*m^2

So according to the father ball’s final velocity along x axis = vfx = 1.44m/s

So according to the father ball’s final momentum along x axis =pfx=m*vfx =0.055kg*1.44m/s = 0.0792kg*m/s

So according to the father ball’s final velocity along y axis = vfy = -1.25m/s

So according to the father ball’s final momentum along y axis =pfy=m*vfy =0.055kg*1.25m/s = -0.06875kg*m/s

Total initial momentum = pi = pix + piy = [(0.0792i)-(0.06875j)] kg*m^2

c)

According to mother at maximum height along y axis ball will have velocity = 0m/s. Hence momentum there will be = 0 kg*m/s

So correct option is: Yes, at the top of its arc.

d)

According to father at maximum height along y axis ball will have velocity = 0m/s. Hence momentum along y axis will be = 0 kg*m/s

But ball still moving in x axis with velocity = 1.44 m/s, hence momentum along x axis is not zero

And thus initial momentum have only x direction but no zero.

Thus correct option is: No, because stroller and ball are moving forward with constant speed.

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