Question

Final speed of the platform in situation (ii), i.e. just after $B$ have jumped will be nearly

• A. $7.5m/s$
• B. $5.5m/s$
• C. $4.5m/s$
• D. $2.5m/s$

Answer 1

The correct option is D $2.5m/s$

Given,

$m_A=60kg$

$m_B=40kg$

$m_{plat}=50kg$

Person $A$ jumps first from the platform in the horizontal direction with velocity $v^{\prime }$, after jump person moves with velocity $v=3m/s$ relative to the platform along the horizontal directio,

By the conservation of Linear momentum,

$(m_{plat}+m_B)v^{\prime }=m_A(v-v^{\prime })$

$90v^{\prime }=60(3-v^{\prime })$

$v^{\prime }=\frac{6}{5}m/s$.. . . . . .(1)

After few second, Person $B$ also jumps from the platform in the same direction, the lets consider the velocity of platfom is $v^{\prime \prime }$.

By the conservation of Linear momentum,

$(m_{plat}+m_B)v^{\prime }=m_{plat}{v}^{\prime \prime }-m_B(v-v^{\prime \prime })$

$90\times \frac{6}{5}=50v^{\prime \prime }-40(3-v^{\prime \prime })$

by solving the above equation, we get

$v^{\prime \prime }=2.5m/s$

The correct option is D