[pattyfroman]

Hi, I have a very important Physics question about projectiles. I would appreciate it if you could answer ASAP. Thanks, Patty Froman

Question: What is the maximum range of a cannon that can be fired from the ground at 123 m/s?

Thanks so much for your effort again!

[rudi_in]

Thank you for posting your question to the Ask Me Help Desk.

I will take a stab at this one...
Other experts, please double check my work.

First of all, if we neglect air friction and fire the cannon at a 45º angle we can find the max range.

Based on the velocity of the projectile at 123 m/s we can determine the x and y component velocities.

y component

123sin45 = 86.97 m/s

x component

123cos45 = 86.97 m/s

Now, in flight, the projectile in the vertical is affected by the force of gravity and slows at a rate of 9.8 m/s/s but is unaffected in the horizontal (friction neglected) and therefore has constant acceleration of 0 m/s/s

We use this information to determine the length of time it is the air until it reaches the peak and begins the descent to the ground.

acceleration = (final velocity - initial velocity) ÷ time

-9.8 = (0 - 86.97) ÷ time

-9.8t = -86.97

t = 8.87 seconds

So it takes a total of 8.87 seconds to reach the peak of its path. Due to the parabolic symmetry of the projectile we can say that it will take another 8.87 seconds to reach the ground for a total of 17.74 seconds in flight. During this time, the projectile is moving at a constant horizontal velocity of 86.97 m/s.

We can use this information to calculate the distance.

speed = distance ÷ time

86.97 m/s = distance ÷ 17.74 s

distance = 1542.85 meters

If someone could please check my work that would be awesome as my physics is a little rusty.

[kp2171]

no clue if the numbers match up, but the setup looks good.

patty -

its important you see how this was broken down and not just copy an answer.

this is a problem with 2 dimensions, and you need to consider both to solve the problem. Time in the air, as mentioned, is only affected by gravity (in this simplified problem), so he used the initial speed to determine the y component of the velocity. Then gravity to determine time in air.

then the second component was of course determining distance in the x direction while in the air.

most 2-D problems are something like this... where you need to determine the x and y vectors and then what other info you have (like an acting force, like gravity) to piece toward the right answer.