Projectile Motion - find initial velocity, flight time and max height

kgal

1. The problem statement, all variables and given/known data
a golf ball is shot from a height of 6.5 ft above the ground at an angle of 45° above the horizontal. The ball lands 39 ft and 3 inches downfield. Assuming ideal projectile motion find:
a. Initial velocity
b. flight time
c. maximum height


2. Relevant equations
r = [(v0*cosθ)t ]i + ((v0*sinθ)t - 1/5gt^2)j.


3. The attempt at a solution
I have attached my work (problem 5) but can't seem to know if it correct. I have converted all of my units to metric because gravity is know as 9.8 m/s^2.

TaxOnFear

kgal,
From what I can gather, you don't have enough information given to you to solve for velocity, time of flight and maximum height directly. Try drawing what you see. The best method I use to solve projectile motion problems is to split the problem up into two parts - the object rising, & then falling.

Also, I can't see your work.

kgal

I used the definition of range to solve for initial velocity:
a.R = (v0cosθ)*[(2v0sinθ)/g]
solved for v0 = sqrt (Rg / 2cosθsinθ) = 10.82 m/s.

b. I split the problem into two pieces, the time it takes the ball to reach the horizontal
t1 = 2v0sinθ / g = 23.9 s
Then got stuck on finding out the time it took the ball to drop the remaining 1.98 m...
I tried finding t2 by using r = (v0cos45)t + (v0sin45t - 1/2 gt^2) and solve for t, but got to the point where t was a quadratic equation with 2 answers, t = 3.1 or 0.13 seconds...

c. y max = y0 + (v0sinθ) ^2 / 2g = 4.96 m