Question

7) This time, your mass is 61.1 kg and the sled s mass is 16.2 kg. You re on the sled, initially moving to the west at 9.84 cm/s. From the southern shore, your friend throws a baseball of mass 0.188 kg, which you catch as it s traveling northward with a horizontal velocity component of 34.3 m/s. What will be the sled s (and your) speed after catching the ball?

Answer 1

Since there is no external force applied, So using momentum conservation:

Pi = Pf

So after catching the ball your velocity V will be:

m1*v1 + m2*v2 = (m1 + m2)*V

m1 = mass of you + sled = 61.1 + 16.2 = 77.3 kg and

m2 = mass of ball = 0.188 kg

v1 = initial velocity of m1 = 9.84 cm/sec towards west = (-0.0984 i) m/s

v2 = initial velocity of m2 = 34.3 m/sec towards north = (34.3 j) m/s

So,

77.3*(-0.0984 i) + 0.188*(34.3 j) = (77.3 + 0.188)*V

V = [-7.60632 i + 6.4484 j]/77.488 = (-7.60632/77.488) i + (6.4484/77.488) j

V = -0.09816 i + 0.083218 j

Now final speed will be:

|V| = sqrt ((-0.09816)^2 + (0.083218)^2) = 0.1287 m/sec

your speed after catching the ball = 0.1287 m/sec = 12.87 cm/sec