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Question: A 300 g mass has a velocity of \(( 3 \hat { i } + 4 \hat { j } )\)m/sec at a certain instant. What i...

A 300 g mass has a velocity of (3i^+4j^)( 3 \hat { i } + 4 \hat { j } )m/sec at a certain instant. What is its kinetic energy

A

1.35 J

B

2.4 J

C

3.75 J

D

7.35 J

Answer

3.75 J

Explanation

Solution

v⃗=(3i^+4j^)\vec { v } = ( 3 \hat { i } + 4 \hat { j } ) ∴ v=32+42=5 m/sv = \sqrt { 3 ^ { 2 } + 4 ^ { 2 } } = 5 \mathrm {~m} / \mathrm { s }. So kinetic energy = 12mv2=12×0.3×(5)2=3.75 J\frac { 1 } { 2 } m v ^ { 2 } = \frac { 1 } { 2 } \times 0.3 \times ( 5 ) ^ { 2 } = 3.75 \mathrm {~J}