Question

A girl throws a ball straight up into the air, and it reaches a height of 5m. Assuming g equals 10m/s2 and no energy is converted to heat, what will be the velocity of the ball when she catches it?

Answer 1

The velocity of the ball when she catches it is 10 m/s.

Given:

A girl throws a ball straight up into the air, and it reaches a height of 5m. Assuming g equals 10m/s2 and no energy is converted to heat.

To Find:

The velocity of the ball when she catches it.

Solution:

To find the velocity of the ball when she catches it, we will follow the following steps:

As we know,

At the lowest point from where the object is thrown upward, energy is completely kinetic and at its highest point, all of its kinetic energy is converted to potential energy while at the midpoint ball will have half kinetic and half potential energy.

Kinetic energy formula =

$\frac{1}{2} m {v}^{2}$

Potential energy formula = mgh

According to the question:

h = 5 m

g = 10 m/s²

So,

Kinetic energy at the lowest point = potential energy at the highest point

$\frac{1}{2} m {v}^{2} = mgh$

Now,

Putting values in the above formula we get,

$\frac{1}{2} {v}^{2} = 10 \times 5$

${v}^{2} = 2 \times 10 \times 5 = 100$

$v = \sqrt{100} = 10m {s}^{ - 1}$

Henceforth, the velocity of the ball when she catches it is 10 m/s.

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