Question

A girl at rest at gate of her society which is 3.2 m above the road comes
down the slope AB on a cycle without paddling. [g = 10 N/kg]
(ii) The velocity with which girl reaches point A is
1. 32 m/s
2. 10 m/s
3. 8 m/s
4. Insufficient information to calculate velocity.
(iii) If the mass of the girl is 40 kg then the kinetic energy of the girl at A is
[Assuming no loss of energy.]
1. 1280 J
2. 1600 J
3. 400 J
4. 3200J

Answer 1

In the 1st question, apply WORK-ENERGY THEOREM.

• Work done by all force is equal to change in KINETIC ENERGY of the object.

$W_{gravity} = \Delta KE$

$\implies mgh= \dfrac{1}{2} m {v}^{2} - 0$

$\implies mgh= \dfrac{1}{2} m {v}^{2}$

$\implies gh= \dfrac{1}{2} {v}^{2}$

$\implies v = \sqrt{2gh}$

$\implies v = \sqrt{2 \times 10 \times 3.2}$

$\implies v = \sqrt{64}$

$\implies v = 8 \: m {s}^{ - 1}$

________________________

Now, KE of object:

$KE = \dfrac{1}{2} m {v}^{2}$

$\implies KE = \dfrac{1}{2} \times 40 \times {8}^{2}$

$\implies KE = 20 \times 64$

$\implies KE = 1280 \: joule$

Hope It Helps.

Answer 2

Answer:

the attached picture has answer for (ii)..

answer of (iii)- option 1=1280 J

since there is no loss of energy, the kinetic energy will change into potential energy

mgh = 40×10×3.2 = 1280 J