Question

An object has a kinetic energy of 275 J and a momentum of magnitude 25.0 kg * m/s. Find the (a) speed and (b) mass of the object.

Answer 1

p=25.0 kg * m/s

K_E=275 J

$Ke=\frac{1}{2}mv^2$

$Ke=\frac{1}{2}mv^2⋅\frac{m}{m}$

$Ke=\frac{m^2v^2}{2m}=\frac{(mv)^2}{2m}$

$Ke=\frac{(mv)^2}{2m}$

mv=p

$Ke=\frac{(p)^2}{2m}$

$2m⋅Ke=p^2$

$m= \frac{p^2}{2Ke}=\frac{25^2}{2⋅275}=1.14 kg$

$p=mv$

$v=\frac{p}{m}=\frac{25}{1.14}=22\frac{m}{s}$