Question

A spring-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.

Answer 1

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.

Step-by-step explanation:

Answer 2

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.

Step-by-step 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:

`p_i = 0`

while the total final momentum is:

`p_f = m_l v_l + m_b v_b`

where

`m_l = 0.60 kg` is the mass of the launcher

`m_b = 0.30 kg` is the mass of the ball

`v_l` is the velocity of the launcher

`v_b` is the velocity of the ball

Since the total momentum must be conserved,
`p_i=p_f`, so

`0=m_l v_l + m_b v_b`

Therefore we find

`v_l = - (m_b)/(m_l)v_b = -(0.30)/(0.60)v_b = -(v_b)/(2)`

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.