Chapter 3, Problem 75GP

To determine

The maximum horizontal range of the gun.

Answer to Problem 75GP

The maximum horizontal range of the gun is $39.2\text{m}$ .

Explanation of Solution

Given:

Time of flight of dart, $t=4\text{s}$

Formula Used:

Since the gun is shooting vertically and the upward flight takes half time to move. Consider the vertical direction and calculate the velocity using first law of motion.

$\begin{array}{c}v=u-gt\\ u=\frac{gt}{2}\end{array}$    … (1)

Where,

  $g$ is the gravitational acceleration.

  $u$ is the velocity.

  $t$ is the time to flight.

The expression to calculate the maximum horizontal range of the gun is,

$R=\frac{u^2}{g}$    … (2)

Where,

  $R$ is the range.

Calculation:

Substitute all the values in equation (1).

$\begin{array}{c}u=\frac{\left(4\text{s}\right)\left(9.8\text{m}/{\text{s}}^2\right)}{2}\\ =19.6\text{m}/\text{s}\end{array}$

Substitute all the values in equation (2).

$\begin{array}{c}R=\frac{{\left(19.6\text{m}/\text{s}\right)}^2}{9.8\text{m}/{\text{s}}^2}\\ =39.2\text{m}\end{array}$

Conclusion:

Thus, the maximum horizontal range of the gun is $39.2\text{m}$ .