You throw a softball (of mass 300 g) straight

up into the air. It reaches a maximum altitude
of 10.1 m and then returns to you.
What is the gravitational potential energy
of the softball at its highest position? Assume
the ball departed from and returned to ground
level.
Answer in units of J
29.69J ---^

Assume no energy is lost by the softball while
it is in the air.
What is the kinetic energy of the softball as
soon as it leaves your hand?
Answer in units of J

What is the kinetic energy of the softball when
it returns to your hand?
Answer in units of J

What is the speed of the ball?
Answer in units of m/s

To find the gravitational potential energy of the softball at its highest position, we can use the formula:

Gravitational Potential Energy = mass * gravitational acceleration * height

The mass of the softball is given as 300 g, which we need to convert to kilograms by dividing by 1000:

mass = 300 g / 1000 = 0.3 kg

The gravitational acceleration is a constant value of approximately 9.8 m/s^2.

Now plugging in the values:

Gravitational Potential Energy = 0.3 kg * 9.8 m/s^2 * 10.1 m

Calculating the value:

Gravitational Potential Energy = 29.82 J (rounded to two decimal places)

Therefore, the gravitational potential energy of the softball at its highest position is 29.82 J.

To find the kinetic energy of the softball as soon as it leaves your hand, we can assume that all the potential energy has been converted to kinetic energy (since no energy is lost). So the kinetic energy will be equal to the gravitational potential energy at the highest position, which we found to be 29.82 J.

Therefore, the kinetic energy of the softball as soon as it leaves your hand is 29.82 J.

Similarly, when the softball returns to your hand, it will still have the same amount of kinetic energy as it did when it left your hand. So the kinetic energy of the softball when it returns is also 29.82 J.

To find the speed of the ball, we can use the formula for kinetic energy:

Kinetic Energy = 1/2 * mass * velocity^2

Rearranging the formula to solve for velocity:

velocity = sqrt((2 * kinetic energy) / mass)

Plugging in the values:

velocity = sqrt((2 * 29.82 J) / 0.3 kg)

Calculating the value:

velocity = sqrt(1996 J / 0.3 kg) = sqrt(6653.33 m^2/s^2)

Therefore, the speed of the ball is approximately:

velocity = 81.52 m/s (rounded to two decimal places)

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