A water-balloon launcher with a mass of 2.0 kg is suspended on a wire. It fires a 0.75 kg balloon to the west at a velocity of 14.0 m/s. What is the
resulting velocity of the launcher if the net force on the launcher is equal to
the reaction force?
A. 5.3 m/s east
B. 7.4 m/s east
C. 37.3 m/s east
D. 6.6 m/s west

5.3 ms east

Explanation:

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards