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### 3.4 Example 4

A cannon shot a projectile at 35 degrees from the horizontal, with a velocity of 17 m/s. We want know the maximum altitude, and the range.

Solution with FisicaLab

Select the Kinematic group and, inside this, the Particles module. Erase the content of the chalkboard. And add one element Cannon and one element Stationary reference system. As show the image below:

The end time, is an unknown data, then in the element Stationary reference system write:

tf

t

The data of the maximum altitude and range correspond at different times. Then, we need first set the problem to determine the maximum altitude, and after set the problem to determine the range.

Maximum altitude

To this case, to the element Cannon write:

Name

Projectile

ax

0

ay

-9.81

xi

0

yi

0

vi

17

angi

35

ti

0

xf

xf

yf

yf

vf

vf

angf

0

The acceleration in X axis is 0, but in Y is -9.81 (the acceleration of gravity). We assume that the cannon shot at time 0. And that this is located at the origin of the stationary system. Also, we know that, at the maximum altitude, the angle of the velocity vector is 0.

Now click in the icon Solve to get the answer.

```xf = 13.842 m ;  yf = 4.846 m ;  vf = 13.926 m/s ;
t = 0.994 s ;
Status = success.

```

The desired data is yf = 4.846 m.

Range

There are many ways to calculate the range. Here, we write to the end Y coordinate 0, and to the final velocity and the end angle write unknown data. This is necessary to satisfied numbers of equations = numbers of unknown data. Then, write:

Name

Projectile

ax

0

ay

-9.81

xi

0

yi

0

vi

17

angi

35

ti

0

xf

xf

yf

0

vf

vf

angf

angf

Now click in the icon Solve to get the answer:

```xf = 27.683 m ;  vf = 17.000 m/s ;  angf = -35.000 degrees ;
t = 1.988 s ;
Status = success.

```

NOTE: If you want the altitude in other position, keep in mind that, in general, are two solutions. The first when the projectile is ascending and the second when the projectile is descending. If you want the second position, you need set the initial position (the start position) after the first position.

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