SOLUTION: 3) Suppose you throw a baseball straight up at a velocity of 64 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. Thi

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 3) Suppose you throw a baseball straight up at a velocity of 64 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. Thi      Log On


   

Question 31632: 3) Suppose you throw a baseball straight up at a velocity of 64 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
• 16 represents 1/2g, the gravitational pull due to gravity (measured in feet per second2).
• v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
• s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.
1. How long will it take to hit the ground?
2. What is the maximum height of the ball? What time will the maximum height be attained?

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Using the given function:
s%28t%29+=+-16t%5E2+%2B+%28vo%29t+%2B+so and substituting vo = 64 ft/sec. and so = 0
s%28t%29+=+-16t%5E2+%2B+64t Set s(t) = 0 and solve for t to find the time at which the baseball will return to the ground.
0+=+-16t%5E2+%2B+64t Solve for t. First factor out a t.
0+=+t%28-16t+%2B+64%29 Apply the zero products principle.
t+=+0 This is the initial condition when the height, s = 0.
0+=+-16t+%2B+64 Add 16t to both sides of the equation.
16t+=+64 Divide both sides by 16.
t+=+4Secs.
1) The ball returns to the ground in 4 seconds.
The maximum height of the ball can be found by finding the location of the verttex of the parabola that is represented by the original quadratic equations%28t%29+=+-16t%5E2+%2B+64t
The t-coordinate of the vertex is given byt+=+%28-b%29%2F2a
The a and b come from the standard form of a quadratic equationax%5E2%2Bbx%2Bc=0
In this problem, a = -16, b = 64, and c = 0
t+=+%28-64%29%2F2%28-16%29
t+=+%28-64%29%2F-32
t+=+2Secs. This is the time at which the baseball reaches its maximum height.
To find the maximum height, substitute this value of t into the original equation and solve for s.
s%282%29+=+-16%282%29%5E2+%2B+64%282%29
s%282%29+=+-64+%2B+128
s%282%29+=+64Feet. This is the maximum height attained by the baseball.