Answer:
[tex]v = 14.78m/s[/tex]
Explanation:
Given
[tex]KE = 150J[/tex]
[tex]p = 20.3kgm/s[/tex]
Required
Determine the object's speed
Kinetic Energy is calculated as:
[tex]KE = \frac{1}{2}mv^2[/tex]
Make m the subject
[tex]m = \frac{2KE}{v^2}[/tex]
Momentum is calculated as:
[tex]p = mv[/tex]
Make m the subject
[tex]m = \frac{p}{v}[/tex]
So, we have:
[tex]m = \frac{p}{v}[/tex] and [tex]m = \frac{2KE}{v^2}[/tex]
Equate both expressions: [tex]m = m[/tex]
[tex]\frac{2KE}{v^2} = \frac{p}{v}[/tex]
Multiply both sides by v
[tex]v * \frac{2KE}{v^2} = \frac{p}{v}*v[/tex]
[tex]\frac{2KE}{v} = p[/tex]
Make v the subject
[tex]v = \frac{2KE}{p}[/tex]
Substitute [tex]KE = 150J[/tex] and [tex]p = 20.3kgm/s[/tex]
[tex]v = \frac{2 * 150}{20.3}[/tex]
[tex]v = \frac{300}{20.3}[/tex]
[tex]v = 14.78m/s[/tex]
