Alana asked in Science & MathematicsPhysics · 3 weeks ago

What is the speed of a 0.149 kg baseball if its kinetic energy is 108 J ?

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• MyRank
Lv 6
3 weeks ago

Given,

Mass (m) = 0.149 kgKinetic Energy (K.E) = 108JSpeed (v) = ?We know that:-Kinetic Energy (K.E) = ½mv²108J = ½ x 0.149kg x v²(108 x 2) = 0.149 x v²Speed (v) = √216/0.149 = 38.07m/sec ≈ 38.1m/sec∴ speed (v) = 38.1m/sec.

• oubaas
Lv 7
3 weeks ago

V = √2E/m = √216/0,149 = 38.1 m/sec

• alex
Lv 7
3 weeks ago

Formula

KE = ½ * m * v^2

• 3 weeks ago

The following is used to calculate the kinetic energy.

KE = ½ * m * v^2

108 = ½ * 0.149 * v^2

v = √(216 ÷ 0.149)

The speed is approximately 38.1 m/s.

• 3 weeks ago

KE = (1/2) * m * v^2

KE is measured in Joules

m is measured in kg

v is measured in m/s

108 = (1/2) * 0.149 * v^2

216 / 0.149 = v^2

216 * 1000 / 149 = v^2

36 * 6 * 100 * 10 / 149 = v^2

36 * 100 * 2 * 2 * 3 * 5 / 149 = v^2

36 * 4 * 100 * 15 * 149 / 149^2 = v^2

(6 * 2 * 10 / 149) * sqrt(15 * 149) = v

v = (120/149) * sqrt(2250 - 15)

v = (120/149) * sqrt(2235)

2209 = 47^2

2235 = 2209 + 24

2235 = (47 + h)^2

2235 = 2209 + 94 * h + h^2

24 = 94h + h^2

h is going to be between 0 and 1, so h^2 will also be between 0 and 1

24 = 94h + 0 , 94h + 1

23/94 , 24/94 = h

23/94 < h < 24/94

23/94 is just under 0.25 and 24/94 is just over 0.25

47.25 seems like a fine compromise for sqrt(2235)

120 * 47.25 / 149

12 * 472.5 / 149

6 * 945 / 149

3 * 1890 / 149

5670 / 149

(5670/149) * (150/150) =>

(5670/150) * (150/149)

5670/150 =>

567/15 =>

1134/30 =>

113.4/3 =>

(111 + 2.4)/3 =>

37 + 0.8 =>

37.8

37.8 * (150/149)

Add another 150th of 37.8.  It'll be closely enough

37.8 * (1 + 1/150) =>

37.8 + 37.8/150 =>

37.8 + 75.6/300 =>

37.8 + 0.25, roughly =>

38.05

Take it to 3 sf

38.1 m/s

Check with a calculator.  All of this was to show that a calculator isn't necessary.

‭38.074459018221143233445144078044‬....

So we're good.