#390 A rock with a mass of 2.80 kg is moving

A rock with a mass of 2.80 kg is moving - Physics

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Free Chegg Question

A rock with a mass of 2.80 kg is moving with velocity

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Free Chegg Answer 

The mass of the body = 2.80 kg

velocity = 5.60 i - 1.40j m/s

The Kinetic Energy of rock at this velocity = 

= (1/2) x 2.80x [(5.60i - 1.4j) . (5.60 i- 1.4j)]

= (1/2) x 2.80 x [5.60x 5.60 +1.4 x 1.4]

=(1/2) x 2.80 x [31.36 + 1.96]

= 0.5 x 2.80 x 33.32

= 46.648 J

Note :

Vectors i.i = j.j = k.k = 1

i.j = j.k= i.k = 0

(b)

The net workdone on the body is equal to chanege in kinetic energy.

We have mass = 2.80 kg

Initial Velocity = (5.60 i - 1.4j) m/s

Final velocity = (8.0i + 4.0j)

Total workdone = Change in Kinetic Energy

= Final Kinetic Energy - Initial Kinetic Energy

= (1/2) m (V_f² - V_i²)

= 0.5 x 2.80 x[(8.0i + 4.0j)² - (5.60 i - 1.4 j)² ]

V_i = Sqrt ( 5.60² +1.4²)

= Sqrt ( 31.36 + 1.96)

= Sqrt (33.32}

= 5.77 m/s

V_f = Sqrt (8.0² + 4.0²)

= Sqrt (64 + 16)

= Sqrt (80)

= 8.94 m/s

Therefore Total workdone = 0-5 x 2.80 x [ 80.0 - 33.32]

= 0.5 x 2.80 x 46.68

= 65.352 J