Question

05
Find the kinetic energy of a ball of mass 4 kg which is
i) moving downwards with the speed of 5 m/s
ii) moving upwards with the speed of 5 m/s
-100 J and +100)
O Both are 100)
0-50 J and 50)
O Both are 50​

Answer 1

Solution: Option D) that is Both are 50 Joule is absolutely correct!

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Proper question: Find the kinetic energy of a ball of mass 4 kg which is

• (i) Moving downwards with the speed of 5 m/s

• (ii) Moving upwards with the speed of 5 m/s

★ In the case 1st...

Provided that:

• Mass of ball = 4 kg

• Moving (downward) with speed = 5 m/s

To calculate:

• Kinetic energy

Solution:

• Kinetic energy = +50 J

Using concept:

• Kinetic energy formula

Using formula:

• ${\small{\underline{\boxed{\sf{E_k \: = \dfrac{1}{2} \: mv^2}}}}}$

Where, E_k denotes kinetic energy, m denotes mass, v denotes velocity.

Required solution:

$:\implies \sf E_k \: = \dfrac{1}{2} \: mv^2 \\ \\ :\implies \sf E_k \: = \dfrac{1}{2} \times 4 \times (5)^{2} \\ \\ :\implies \sf E_k \: = \dfrac{1}{2} \times 4 \times 5 \times 5 \\ \\ :\implies \sf E_k \: = \dfrac{1}{2} \times 4 \times 25 \\ \\ :\implies \sf E_k \: = 2 \times 25 \\ \\ :\implies \sf E_k \: = 50 \: J \\ \\ :\implies \sf Kinetic \: energy \: = 50 \: Joules$

★ In the case 2nd..

Provided that:

• Mass of ball = 4 kg

• Moving (upward) with speed = 5 m/s

To calculate:

• Kinetic energy

Solution:

• Kinetic energy = +50 J

Using concept:

• Kinetic energy formula

Using formula:

• ${\small{\underline{\boxed{\sf{E_k \: = \dfrac{1}{2} \: mv^2}}}}}$

Where, E_k denotes kinetic energy, m denotes mass, v denotes velocity.

Required solution:

$:\implies \sf E_k \: = \dfrac{1}{2} \: mv^2 \\ \\ :\implies \sf E_k \: = \dfrac{1}{2} \times 4 \times (5)^{2} \\ \\ :\implies \sf E_k \: = \dfrac{1}{2} \times 4 \times 5 \times 5 \\ \\ :\implies \sf E_k \: = \dfrac{1}{2} \times 4 \times 25 \\ \\ :\implies \sf E_k \: = 2 \times 25 \\ \\ :\implies \sf E_k \: = 50 \: J \\ \\ :\implies \sf Kinetic \: energy \: = 50 \: Joules$

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Why I didn't add negative sign in Case 2nd as it's moving upwards?

Do you remember kinetic energy never be negative!? Yes, kinetic energy is that energy that can't be negative, it is just still positive! That's the reason the answer is +50 J in both the conditions!