Chapter 6.1, Problem 2PP

To determine

Horizontal velocity of the giraffes.

Answer to Problem 2PP

  $1.143\text{m/s}$

Explanation of Solution

Given:

Horizontal distance is $x=0.4\text{m}$

Vertical height is $y=0.6\text{m}$

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 the toy can be obtained by:

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

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

Horizontal displacement of the toy:

  $x=u_{x}t$ ….. (2)

Where, $u_x$ is the horizontal velocity.

From equation (1)

As initial vertical velocity is $u_y=0\text{m/s}$

So, $t=\sqrt{\frac{-2y}{g}}$

Now putting $t$ in equation (2)

  $\begin{array}{l}x=u_x\sqrt{\frac{-2y}{g}}\\ u_x=\frac{x}{\sqrt{\frac{-2y}{g}}}\\ =\frac{0.4}{\sqrt{\frac{-2\left(-0.6\right)}{9.8}}}\\ =1.143\text{m/s}\end{array}$

Conclusion:

So, horizontal velocity of the giraffesis $1.143\text{m/s}$ .