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  1. You serve a volleyball with a mass of 1.7 kg. The ball leaves your hand with
    a speed of 27 m/s. The ball has
    energy. Calculate.
    2. A cinder block is sitting on a platform 18 m high. The mass is 8.06 kg. The
    ball has
    energy. Calculate.
    3. There is a bell at the top of a tower that has a mass of 19.4 kg, it has 3802
    of potential energy. What height is the bell located at?

Verified Answer :

GinnyAnswer

Of course! Let's break down and solve each part of the problem step-by-step:

### Part 1: Kinetic Energy of the Volleyball

1. We are given the mass of the volleyball: \(\( m = 1.7 \)\) kg.
2. We are also given the speed of the volleyball: \(\( v = 27 \)\) m/s.

The formula for kinetic energy \(\( KE \)\) is:
\(\[ KE = \frac{1}{2} m v^2 \]\)

Substitute the given values into the formula:

\(\[ KE = \frac{1}{2} \times 1.7 \times (27)^2 \]\)

When you calculate this, you get:

\(\[ KE = 0.5 \times 1.7 \times 729 \]\)
\(\[ KE = 0.85 \times 729 \]\)
\(\[ KE = 619.65 \]\)

So, the kinetic energy of the volleyball is 619.65 Joules.

### Part 2: Potential Energy of the Cinder Block

1. We are given the mass of the cinder block: \(\( m = 8.06 \)\) kg.
2. The height at which the cinder block is located: \(\( h = 18 \)\) m.
3. The acceleration due to gravity \(\( g \)\) is \(\( 9.81 \)\) m/s\(\(^2\)\).

The formula for potential energy \(\( PE \)\) is:
\(\[ PE = m g h \]\)

Substitute the given values into the formula:

\(\[ PE = 8.06 \times 9.81 \times 18 \]\)

When you calculate this, you get:

\(\[ PE = 8.06 \times 9.81 \times 18 \]\)
\(\[ PE = 1423.2348 \]\)

So, the potential energy of the cinder block is 1423.2348 Joules.

### Part 3: Height of the Bell

1. We are given the potential energy of the bell: \(\( PE = 3802 \)\) Joules.
2. The mass of the bell: \(\( m = 19.4 \)\) kg.
3. The acceleration due to gravity \(\( g \)\) is \(\( 9.81 \)\) m/s\(\(^2\)\).

We need to find the height \(\( h \)\). The formula for height derived from the potential energy formula is:

\(\[ h = \frac{PE}{mg} \]\)

Substitute the given values into the formula:

\(\[ h = \frac{3802}{19.4 \times 9.81} \]\)

When you calculate this, you get:

\(\[ h = \frac{3802}{190.314} \]\)
\(\[ h = 19.977510850489193 \]\)

So, the height at which the bell is located is 19.977510850489193 meters.

Thus, we have calculated the following results:
1. The kinetic energy of the volleyball is 619.65 Joules.
2. The potential energy of the cinder block is 1423.2348 Joules.
3. The height of the bell is approximately 19.98 meters.

I hope this answer helps! Please let me know if you need further assistance.

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