Question

When a body is thrown vertically upwards with a velocity 50 m/s, the percentage of its initial kinetic energy converted to potential energy after 4s is (g=10m/s2)

Answer 1

96% is the answer

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Answer 2

Answer:

The percentage of its initial kinetic energy is 96%.

Explanation:

As per the question we have,

The initial velocity of the body=50m/s

The time in which the kinetic energy is converted to potential energy=4 seconds

The acceleration due to gravity(g)=10m/s²

The initial kinetic energy

It is calculated as

$K_1=\frac{1}{2}mu^2$    (1)

Where,

K₁=initial kinetic energy

m=mass of the body

u=initial velocity of the body

We obtain by entering the values into equation (1);

$K_1=\frac{1}{2}m\times (50)^2$

$K_1=1250m$     (2)

The final kinetic energy

It is calculated as

$K_2=\frac{1}{2}mv^2$    (2)

Where,

K₂=final kinetic energy

v=final velocity

The final velocity is calculated from the first equation of motion. Which is given as,

$v=u+at$    (3)

By entering the necessary values in equation (3), we obtain;

$v=50-10\times 4$

$v=50-40$

$v=10\ m/s$   (4)

We obtain this by entering the numbers in equation (2);

$K_2=\frac{1}{2}\times m\times (10)^2$

$K_2=50m$    (5)

The percentage of its initial kinetic energy is calculated as,

$\frac{K_1-K_2}{K_1}\times 100$   (6)

By entering the values into equation (6), we obtain;

$\frac{1250m-50m}{1250m}\times 100$

$\frac{1200m}{1250m}\times 100$

$=96\%$

Hence, the percentage of its initial kinetic energy is 96%.

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