Chapter 6.1, Problem 3PP

To determine

Vertical distance from the edge of the counter.

Answer to Problem 3PP

  $\text{0}\text{.6}\text{cm}$

Explanation of Solution

Given:

Initial horizontal velocity of sundaes is $u_x=2\text{m/s}$

Initial vertical velocity of sundaes is $u_y=0\text{m/s}$

Horizontal distance from the edge of the counter is $x=7\text{cm}$

Formula Used:

Second equation of motion:

  $s=ut+\frac{1}{2}a{t}^2$

Where, u is the initial velocity, t is the time, a is the acceleration and s is the displacement.

Calculation:

Vertical displacement of sundaes:

  $y=u_{y}t-\frac{1}{2}g{t}^2$ ….. (1)

Where, $u_y$ is the initial velocity is vertical direction and g is the acceleration due to gravity.

Horizontal displacement of sundaes:

  $x=u_{x}t$ ….. (2)

Where, $u_x$ is the horizontal velocity.

From (2)

  $t=\frac{x}{u_x}$

As $u_y=0\text{m/s}$

So, putting $t$ in (1)

  $\begin{array}{c}y=-\frac{1}{2}g{\left(\frac{x}{u_x}\right)}^2\\ =-\frac{1}{2}\times 9.8\times {\left(\frac{0.07}{2}\right)}^2\\ =0.006\text{m}\\ \text{= 0}\text{.6}\text{cm}\end{array}$

Conclusion:

So, vertical distance from the edge of the counter is $\text{0}\text{.6}\text{cm}$ .