The angle and distance of a projection - Grade 11 physics

[CAT 2]

Homework Statement

A water balloon is fired 34 m/s from a water cannon, which is aimed at an angle of 18° above the ground. The centre of the cannon's target (which has a radius of 1.0m) is painted on the asphalt 42m away from the water cannon.
a) Will the balloon hit the target? Justify your response with calculations that indicate where the water balloon will land.
b) make one suggestion about how to adjust the water cannon so that the water balloon will hit the target. Justify your choice.

Homework Equations

This equation is used for finding horizontal distance.
Dh = v1^2 Sin 2(angle)/ a

The Attempt at a Solution

. https://www.physicsforums.com/file:///C:/Users/User/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png v1 = 34 m/s
angle = 18°
a = 9.8 m/s^2 [down]

Find the horizontal projected distance of the projected balloon

Dh = v1^2 Sin 2(angle)/ a
Dh = (34 m/s)^2 (Sin2(18°)/ 9.8 m/s^2
Dh = 69.3 meters

Since the distance to the target is 42 meters and the water balloon traveled 69.3 meters, the balloon did not hit the target.To make it hit the target, the speed needs to be decreased.

Dh = v1^2 Sin 2(angle)/ a
42m = v1^2 (Sin2(18°)/ 9.8 m/s^2
42m = v1^2 (0.05998)
√700 = v1
26.5 m/s = v1To make the balloon hit the target the speed needs to be decreased to 26.5m/s.Is this done correctly?

 

[gneill]

Looks good.

What other parameter might you vary to change the range of the water canon? Which parameter might be easier to vary accurately (on a real water canon)?

 

[CAT 2]

The angle would probably have been a better choice, but it was easier to adjust the speed. They don't exactly specify which one to change, (speed or angle). Do you think it will matter?

 

[gneill]

The angle would probably have been a better choice, but it was easier to adjust the speed. They don't exactly specify which one to change, (speed or angle). Do you think it will matter?

Probably not in a purely technical sense. But I would think that practically speaking, a canon would have targeting swivels (altitude and azimuth) built into its design, and simple to adjust. Changing the "charge" of a shot might be more cumbersome.

 

[CAT 2]

Yeah, that's true. Thanks for your help.