Chapter 6, Problem 36P

To determine

Part(a)

The speed of the ball at the highest point

Answer to Problem 36P

Solution: 0

Explanation of Solution

Given:

Mass of ball is 0.48 kg.

Initial speed is 8.8 m/s.

The angle of projection is 36 degrees.

Formula used:

Potential Energy is given by

  $PE=mgh$

Where m is massandhis height.

Calculation:

At the highestpoint, the ball has only potential energy, so the velocity at the highest point is zero.

Conclusion:

From the above explanation, the ball will have 0 velocities at the highest point.

Part(b)

To Determine:

Maximum height attained by the ball

Solution:

1.37 m

Given:

Mass of ball is 0.48 kg. Initial speed is 8.8 m/s. The angle of projection is 36 degrees.

Formula used:

The kinetic energy of an object is given by

  $KE=\frac{1}{2}m{v}^2$

Potential Energy is given by

  $PE=mgh$

Where m is mass, v velocity, h is height.

Calculation:

At the highestpoint, the kinetic energy is converted to potential energy.

Applying conservation of energy

  $\begin{array}{l}\frac{1}{2}m{v}^2=mgh\\ v=u\sin 36°\end{array}$

  $h=\frac{v^2}{2g}$

Where only the vertical component of velocity will act so velocity will be $\text{u sin 36}°$

Substituting the values

  $h=\frac{{\text{(8}\text{.8×sin}\text{36°)}}^2}{\text{2×9}\text{.8}}$

  $h=1.\text{37 m}$

Conclusion:

From the above explanation, Maximum height attained by the ball is 1.37 m.