Question

A rubber ball of mass 25g falls from a height of 2m and rebounds to a height of 1.5 m. find the impulse

Answer 1

A rubber ball of mass 25g or 0.025kg falls from height of 2m as shown in figure .
initial velocity of rubber ball , u = 0
Let v is the final velocity ,
Then, use formula,
V² = u² + 2aS
Here , S = 2m , g = 10m/s²
∴ v² = 2 × 10 × 2 = 40 ⇒v = 2√10 m/s

Now, rubber ball rebounds to height of 1.5 m .
e.g., at height of 1.5m , velocity of rubber ball, v = 0
Let intial velocity is u
Now, v² = u² + 2as
Here, v = 0, a = - 10m/s² , s = 1.5m
∴u² = 2 × 10 × 1.5 = 30 ⇒u = √30 m/s

Now, impulse = change in momentum
initial momentum of rubber ball = mv
Final momentum of rubber ball = -mu [ ∵ direction of motion of ball are opposite ]
Hence, impulse = mv -(-mu) = m(v+u)
= 0.025 × (2√10 + √30) kgm/s
=0.2948 Kgm/s

Answer 2

Attached above, hope you satisfied with my answer.