Question

at certain point the K.E and P.E of a body of mass 0.1kg moving vertically up are 3.6J and 6.2J.it rises to a maximum height of

Answer 1

We know that the total energy is conserved,

Hence, Kinetic Energy(KE) + Potential Energy(PE)  = Total Energy

Since at maximum height, the object is at rest and no kinetic energy exists,

Therefore,

KE + PE₁ = PE₂

3.6 + 6.2 = mgh

9.8 = (0.1)(9.8)h

Therefore, h = 10m

Answer 2

Answer:

The maximum height attained by the body is 9.8m.

Explanation:

The values given in the question are,

K.E.=3.6J

P.E.=6.2J

The mass of the body(m)=0.1kg

We know that the kinetic energy is given as,

$K.E.=\frac{1}{2}mv^2$

So,

$3.6=\frac{1}{2}\times 0.1\times v^2$

$v^2=72m/s$      (1)

And the potential energy is given as,

$P.E.=mgh$     (g=acceleration due to gravity=10m/s²)

$6.2=0.1\times 10\times h$

$h=6.2m$   (2)

We can deduce the third equation of motion as follows:

$v^2-u^2=-2gh$   (3)

Inserting the entities in equation (3) we get;

$72-u^2=-2\times 10\times 6.2$

$u^2=196m/s$     (4)

The final velocity is zero at maximum height.

So,

$H_m_a_x=\frac{u^2}{2g}$    (5)

By placing values in equation (5) we get;

$H_m_a_x=\frac{196}{2\times 10}$

$H_m_a_x=9.8\ m$

Hence, the maximum height attained by the body is 9.8m.

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