Chapter 6, Problem 8STP

To determine

To Find: Will the performer need to adjust their canon so that ball will land inside the ring instead of past it.

Answer to Problem 8STP

Yes, performers need to displace the canon by $1.5\text{m}$ towards right side in order to make the ball land inside the ring.

Explanation of Solution

Given:

Horizontal velocity of the ball $=25\text{m/s}$

Height $=52\text{m}$

Horizontal distance $=80\text{m}$

Formula used:

Distance travelled can be calculated as:

  $x=v_{x}t$

Where,

  $v_x$ is the velocity along x-axis

  $t$ is the time taken

Calculation:

Time taken by ball to reach the ground from the given height can be calculated as:

  $y=v_{y}t+\frac{1}{2}g{t}^2$

Where,

  $y$ is the height

  $v_y$ is the velocity along vertical direction

  $t$ is the time taken

  $g$ is the gravitational acceleration

  $\begin{array}{l}y=v_{y}t+\frac{1}{2}g{t}^2\\ 52=0+\frac{1}{2}\times 9.8\times t^2\\ t=\sqrt{10.6}\\ t=3.26\text{s}\end{array}$

Now, horizontal distance covered by the ball is

  $\begin{array}{l}x=v_{x}t\\ x=25\times 3.26\\ x=81.5\text{m}\end{array}$

Conclusion:

Since the distance travelled by the ball is greater than the diameter of the ring.

Therefore, it will not land inside the ring.

Keep the distance of $1.5\text{m}$ between the cannon and the ring so that ball can land inside the ring.