Question

How much momentum will a box of mass 10kg transfer to the floor if it falls from a height of 80cm ? Take its downward acceleration to be 10 m/s^2

Answer 1

$\textit{ \textbf{ Hello Mate! }}$

Converting 80 cm into m we get

80 cm = 80 / 100 m or 0.8 m

Here, u = 0
s = 0.8 m
a = 10 m/s^2

${v}^{2} - {u}^{2} = 2as \\ {v}^{2} - {0}^{2} = 2(10)(0.8) \\ v = \sqrt{16} \\ v = 4 \: \frac{m}{s}$

Momentum = Mass × Velocity

p = mv

p = ( 0.8 kg ) × ( 4 m/s )

p = 3.2 kg m/s

$\boxed{ \textsf{ Momentum\:transferred\:is\:3.2\:kg\:m/s }}$

Have great future ahead!

Answer 2

$\textbf{\huge{Hey there!}}\\\\Given,\\Initial \ velocity(u) = 0 \ m/s\\Distance(s) = 80 \ cm \ = 0.8\  m\\Acceleration(a) = 10 \ m/s^2\\\\\textbf{\underline{By 3rd equation of motion:}}\\v^2 - u^2 = 2as\\v^2 - 0^2 = 2\times 10 \times 0.8\\v^2 = 16\\v =\sqrt{16}\\v = 4 \ m/s\\\\We\  know,\\\boxed{\bold{Momentum = Mass \times Velocity}}\\\rho = m\times v\\\rho = 0.8 \times 4\\\rho = 3.2 \ kg \ m /s\\\\\boxed{\boxed{\textbf{Momentum = 3.2 kg m/s}}}\\\\\text{Hope It Helps You!}$