I need to calculate the max height and distance (at the max height) of a ball travelling 33.6m/s 30 degrees above the x-axis.(adsbygoogle = window.adsbygoogle || []).push({});

The max height was no problem, but I tried finding the distance using an arc length equation (with respect to time) and it didn't work. My distance was shorter than my displacement.

Now, I'm assuming it didn't work because in place of:

L= int(sqrt(1+(f'(x))^2))dx

(L=arc length)

I used:

d=int(sqrt(1+(x'(t))^2))dt=int(sqrt(1+(v(t))^2))dt

(d=distance, x(t)=displacement function, v(t) velocity function)

and this assumes uniform acceleration, but maybe the equation didn't work because though my acceleration is -9.8 in the y-direction, the object's direction is constantly changing, making my acceleration not uniform? This is just a guess though.

Bottom line: all I really need is a good equation that I can use to find the DISTANCE (not displacement) that the ball travels. Any help would be MUCH appreciated!

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# Projectile motion equation question (2D)

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