Follow the three steps and instructions shown in Fig. 5 to play the toy \" Astro

Question

Follow the three steps and instructions shown in Fig. 5 to play the toy " AstroBlaster", in wh Step 3 shows that the smallest ball (red) will reach a height of h Assume all the collisions are elastic and the air resistance can be neglected. Use the energy 2. ich the and momentum conservation laws to prove: hs-|-| h0 >> ho , where M and m are the masses of the AstroBlaster and the smallest red ball respectively. ho Step 1: Hold tip of AstroBlaster's rod which extends through the smallest ball (red). Hold away from body at arm's length Step 2: Relcase when AstroBlaster is hanging straight down. Step 3. The smallest ball (red) will reach a height of h The drop height is Figure 5. Play the toy AstroBlaster in three steps

Explanation / Answer

Initial velocity of M, u = 0
Consider v be the final velocity of M
Using the equation v2 - u2 = 2gh,
Where g is the acceleration due to gravity and h is the height from which it is dropped.
v2 - 0 = 2gho
v2 = 2gho         ...(1)

Consider the moment just after the collision. M will still have the velocity v since the collision is elastic. Soon after the collision, consider that m will move up with a velocity v' and the rest of the M will remain at rest
Since momentum is conserved,
Mv = - mv' + (M - m) x 0
Mv = - mv'          ....(2)
For m, v' is the initial velocity and its final velocity after reaching hB will be zero.
0 - (v')2 = 2(-g)hB
v'2 = 2ghB     ...(3)

Squaring (2),
M2v2 = m2v'2
Substituting (1) and (3),
M22gho = m22ghB
hB = (M/m)2 ho

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