Question

Erica (39kg \;kg ) and Danny (45kg \;kg ) are bouncing on a trampoline. Just as Erica reaches the high point of her bounce, Danny is moving upward past her at 4.8m/s \; m/s . At that instant he grabs hold of her.
What is their speed just after he grabs her?

Answer 1

Answer:

2.57142857143 m/s

Explanation:

$m_1$ = Mass of Danny = 45 kg

$m_2$ = Mass of Erica = 39 kg

$u_1$ = Velocity of Danny = 4.8 m/s

v = Combined velocity

In this system the linear momentum is conserved

$m_1u_1=(m_1+m_2)v\\\Rightarrow v=\dfrac{m_1u_1}{m_1+m_2}\\\Rightarrow v=\dfrac{45\times 4.8}{39+45}\\\Rightarrow v=2.57142857143\ m/s$

The speed of Erica and Danny is 2.57142857143 m/s