Acannon ball at ground level is aimed 30 above the horizontal and is fired with an initial speed of 125 m/s. how far away from the cannon will the cannonball hit the ground?

691 m

Explanation:

In these problems the time a ball is in the air is determined by the gravitational acceleration (y-coordinate) and the distance it travels is related to the velocity in the x-coordinate.

First get the x and y components of the initial speed.

Initial speed has a magnitude of 125 and a direction of 30°

speed in x = 125 cos 30° = 108.3 m/s

speed in y = 125 sin 30° = 62.5 m/s

The time it takes to the ball to reach the highest height (when the speed in the y-coordinate is 0) is:

0 = 62.5 - 9.8*t

t = 6.38 s

With the time you can calculate the distance travelled in the x-coordinate at a constant speed of 108.3.

d = vt

d = 108.3 * 6.38

d = 691 m

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