Chapter 3, Problem 55GP

To determine

Horizontal and vertical component of truck.

Answer to Problem 55GP

The horizontal and vertical components are $\text{4}{\text{.60 m/s}}^2\text{ and 3}{\text{.06 m/s}}^2$

Explanation of Solution

Given:

  $\begin{array}{l}u=120\text{ km/hr}\\ u=\frac{120\times 1000}{30\times 60}=\frac{100}{3}\text{ m/s}\end{array}$

Formula Used:

  $v=u+at$

Calculation:

Substituting the values,

  $\begin{array}{c}0=\frac{100}{3}-a\left(6\right)\\ a=\frac{100}{18}\\ =\frac{50}{9}{\text{m/s}}^2\end{array}$

The given situation is shown below.

  

Horizontal component,

  $\begin{array}{c}a\cos 32°=\frac{50}{9}\cos 32°\\ =4.63{\text{ m/s}}^2\end{array}$

Vertical component,

  $\begin{array}{c}a\sin 32°=\frac{50}{9}\sin 32°\\ =3.06{\text{ m/s}}^2\end{array}$

Conclusion:

The horizontal and vertical components are $\text{4}{\text{.60 m/s}}^2\text{ and 3}{\text{.06 m/s}}^2$