SOLUTION: I have been struggling with this problem for a week and I just confuse myself more and more- so thank you in advance for your help! The word problem is: Suppose the height of a gol

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I have been struggling with this problem for a week and I just confuse myself more and more- so thank you in advance for your help! The word problem is: Suppose the height of a gol      Log On


   

Question 11365: I have been struggling with this problem for a week and I just confuse myself more and more- so thank you in advance for your help! The word problem is: Suppose the height of a golf ball is described after initial velocity from the groud of 4.9 m/sec.
a) write the equation for describing the height of the ball after t seconds.
b) predict how long it will be before the ball returns to the ground.
c) when does the golf ball reach its highest point?
d) how high will the golf ball be at that time?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Well, I'm not surprised to hear that you have been struggling with this problem. You seem to missing the description of the golf ball's behavior following its initial (upward?) velocity from the ground.
The formula is:
h%28t%29+=+-4.9t%5E2+%2B+%28Vo%29t+%2B+Ho This function describes the height (in meters) of an object propelled upward with an initial velocity of Vo (meter per second) from an initial height of Ho (meters).
a) h%28t%29+=+-4.9t%5E2+%2B+4.9t Since the golf ball is leaving from the ground, the initial height (Ho) is zero.
b) When the golf ball will returns to the ground, its height (h) will be zero.
0+=+-4.9t2+%2B+4.9t Solve for t.
t%28-4.9t+%2B+4.9%29+=+0
t+=+0 or -4.9t+%2B+4.9+=+0
t = 0 is when the golf ball started it epic journey into spase.
-4.9t+=+-4.9
t+=+1 The ball returns to Earth in 1 second.
c) To find when the ball reaches its zenith (highest point), you need to find the time, t, at the vertex of the parabola.
This can be found by using t = -b/2a (Assuming that you don't use differential calculus).
t+=+%28-4.9%29%2F2%28-4.9%29
t+=+1%2F2
The golf ball reaches its maximum height in 1/2 second.
d) Substitute t = 1/2 second into the original function, h(t) to find its maximum height.
h%281%2F2%29+=+-4.9%281%2F2%29%5E2+%2B+4.9%281%2F2%29 Solve for h.
h%281%2F2%29+=+%28-4.9%2F4%29+%2B+4.9%2F2
h%281%2F2%29+=+-4.9%2F4+%2B+9.8%2F4
h%281%2F2%29+=+4.9%2F4
h%281%2F2%29+=+1.22
The maximum height attained by the golf ball is 1.22... meters.