Chapter 5, Problem 63A

(a)

To determine

The speed of the vehicle while moving along its descent path

Answer to Problem 63A

v = 6.52 m/s

Explanation of Solution

Given:

Vertical component of velocity $v_y=5.5\text{m/s}$ Horizontal component of velocity $v_x=3.5\text{m/s}$

Formula Used:

The resultant velocity is

  $v=\sqrt{v_x{}^2+v_y{}^2}$

Calculation:

The vehicle decent with a speed v , which is the resultant of $v_x\text{and}{v}_y$

  $\begin{array}{l}v=\sqrt{v_x{}^2+v_y{}^2}\\ v=\sqrt{{(5.5)}^2+{(3.5)}^2}\\ v=6.52\text{m/s}\end{array}$

Conclusion:

The speed of the vehicle with which it moves along its descend path v = 6.52 m/s

(b)

To determine

The angle made by the velocity with the vertical

Answer to Problem 63A

θ = 32.5⁰

Explanation of Solution

Given:

Vertical component of velocity ${\text{v}}_{\text{y}}\text{=5}\text{.5m/s}$ Horizontal component of velocity ${\text{v}}_x\text{=3}\text{.5m/s}$

The speed of the vehicle with which it moves along its descend path v = 6.52 m/s

Formula Used:

  $v_y=v\cos \theta$

Calculation:

From the above figure, θ is the angle with respect to vertical

  $\begin{array}{l}{v}_y=v\cos \theta \\ \theta ={\cos }^{-1}\frac{v_y}{v}\\ \theta ={\cos }^{-1}\frac{5.5}{6.52}\\ \theta ={32.5}^0\end{array}$

Conclusion:

The angle made by v with vertical is θ =32.5⁰

(c)

To determine

The time taken by the vehicle to reach the surface

Answer to Problem 63A

t = 41.8 s

Explanation of Solution

Given:

Let d is the distance travelled by the vehicle

The vertical distance of the vehicle d_y =230 m

The angle between d and d_yθ = 32.5⁰

Formula Used:

$\text{time =}\frac{\text{distance}}{\text{speed}}$$$

Calculation:

From the figure

$$

  $\begin{array}{l}{d}_y=d\cos \theta \\ d=\frac{d_y}{\cos \theta }\\ d=\frac{230\text{m}}{\cos {32.5}^0}\\ d=272.7\text{ m}\end{array}$

Time taken by the vehicle to land the surface of Marsis

  $\begin{array}{c}t=\frac{d}{v}\\ \text{= }\frac{272.7\text{m}}{6.52{\text{m/s}}^{\text{2}}}\\ t=41.82\text{ s}\end{array}$

Conclusion:

The vehicle takes 41.82 s to land the surface from a height of 230 m