Answer to Question #123056 in Classical Mechanics for Claire

Question

A man challenges a former minor league baseball player to a snowball fight. The fight ends quickly, the man gets hit in the head by a snowball. Prior to collision, the mans head (5.5kg) was travelling at a rate of 5.0m/s [N]. The snowball (0.250kg) was travelling South 60 degrees of North at the speed of 35 m/s. The snowball sticks to the mans face after collision?

Answer 1

As per the given question,

Mass of the men's head$(m_1)=5.5 kg$

Traveling speed $(v_1)=5 m/sec$

Mass of the snowball$(m_2)=0.25 kg$

Traveling direction of the ball $(\theta)=60^\circ$

speed of the ball $(v_2)=35m/sec$

Collision is perfectly in-elastic,

Now, applying the conservation of momentum,

$m_1v_1+m_2v_2\cos(60)=(m_1+m_2)v$

$\Rightarrow v_y=\frac{5.5\times 5+0.25\times 35 \frac{1}{2}}{5.5+0.25}=5.54 \hat{j}m/sec$ (North direction)

Now horizontal component,

$(m_1+m_2)v=m_2 v_2 \sin(60)$

$\Rightarrow v_x=\frac{m_2 v_2\sin(60)}{m_1+m_2}$

$\Rightarrow v_x=\frac{0.25\times 35 \frac{\sqrt{3}}{2}}{5.5+0.25} \hat{i}m/sec$

$\Rightarrow v_x=1.31\hat{j} m/sec$

Hence, net velocity of the ball,

$v=\sqrt{v_x^2+v_y^2}$

$\Rightarrow v=\sqrt{5.54^2+1.31^2 }=5.7m/sec$