A cannonball is fired from a point 35ft above ground level at an angle of 35 degrees. It hits the ground 100ft away. Calculate its travel time, initial speed, and maximum height above the ground.
initial height = h = 35ft
angle = x = 35 degrees
gravity = g = 32ft/s^2
travel time, initial speed, and max height are unknown.
initial velocity = sqrt[(Range*gravity)/sin(2x)]
Bolds represent vectors. r(t) = position function.
The Attempt at a Solution
I've found the derivative and attempted to find max height, but that didn't work without a velocity. I tried the initial velocity equation I posted but that only works if the initial height and final height are equal. I attempted to find the time and initial velocity by using r(t) = 100i + 0j making it so (v*cosx)ti = 100 and [h+(v*sinx)t-(1/2)gt^2]j = 0 But no matter what I did I would find myself with two unsolved variables.