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A moving object has a kinetic energy of 150J and a momentum of 20.3kgxm/s find the speed of the object in m/s

Sagot :

MrRoyalidn

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]

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