Chapter 5, Problem 10A

a. How far below an initial straight-line path will a projectile fall in one second?

b. Does your answer depend on the angle of launch or on the initial speed of the projectile? Defend your answer.

To determine

The distance below an initial straight-line path travelled by projectile while falling off.

Answer to Problem 10A

The distance below an initial straight-line path travelled by projectile while falling off is $5\text{m}$ .

Explanation of Solution

Given:

The time period is $t=1\text{ s}$ .

Formula used:

The expression for equation of motion under constant acceleration is,

  $s=ut+\frac{1}{2}g{t}^2$

Here, $u$ is the initial velocity, $t$ is the time period, and $g$ is the acceleration due to gravity.

Calculation:

Consider the acceleration due to gravity as $g=9.8\text{m}/{\text{s}}^{\text{2}}$ .

The distance below an initial straight-line path will a projectile fall in one second is,

  $\begin{array}{l}s=ut+\frac{1}{2}g{t}^2\\ s=\left(0\right)\left(1\text{s}\right)+\frac{1}{2}\left(9.8\text{m}/{\text{s}}^{\text{2}}\right){\left(1\text{s}\right)}^2\\ s=5\text{ m}\end{array}$

Conclusion:

Thus, the distance below an initial straight-line path travelled by projectile while falling off in one second is $5.0\text{ m}$ .

To determine

To identify:Whether the distance travelled obtained in part (a) depends on the angle of launch or on the initial speed of the projectile.

Answer to Problem 10A

The distance neither depend on the angle of launch nor on the initial speed of the projectile.

Explanation of Solution

Given:

The time period is $t=1\text{ s}$ .

Formula used:

The expression for equation of motion under constant acceleration is,

  $s=ut+\frac{1}{2}g{t}^2$

Here, $u$ is the initial velocity, $t$ is the time period, and $g$ is the acceleration due to gravity.

Calculation:

The expression for vertical distance below the line is,

  $s=\frac{1}{2}g{t}^2$

Here, $t$ is the time period, and $g$ is the acceleration due to gravity.

The equation of vertical distance is not relative to the angle of launch or the initial speed of the projectile. It is relative to the acceleration due to gravity and the time.

Conclusion:

Thus, the distance doesn’t depend on the angle of launch or on the initial speed of the projectile.