Aspring-loaded launcher has a mass of 0.60  kg and is placed on a platform 1.2m above the ground. the force of friction is negligible between the platform and the launcher. the launcher fires a 0.30kg ball that lands a distance d to the right of the platform, as shown in the diagram above. which of the following explanations is true?
a the launcher will not fall off the platform because only the ball receives an applied force.
b the launcher will fall off the platform and land d3 to the left of the platform because the mass of the system is three times the mass of the ball.
c the launcher will fall off the platform and land d2 to the left of the platform because the launcher is twice the mass of the ball.
d the launcher will fall off the stand and land d to the left of the stand because the force is the same on both objects.

C The launcher will fall off the platform and land D/2 to the left of the platform because the launcher is twice the mass of the ball.

Explanation:

The figure is missing: you can find it in attachment.

We can apply the law of conservation of momentum to check that the launcher will leave the platform with a speed which is half the speed of the ball. In fact, the total initial momentum is zero:

while the total final momentum is:

where

is the mass of the launcher

is the mass of the ball

is the velocity of the launcher

is the velocity of the ball

Since the total momentum must be conserved, , so

Therefore we find

which means that the launcher leaves the platform with a velocity which is half that of the ball, and in the opposite direction (to the left).

Since the distance covered by both the ball and the launcher only depends on their horizontal velocity, this also means that the launcher will cover half the distance covered by the ball before reaching the ground: therefore, since the ball covers a distance of D, the launcher will cover a distance of D/2.

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)