SOLUTION: 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 f

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 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 f      Log On


   

Question 42672This question is from textbook College Algebra
: 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.
a) What is the function that describes this problem?
b) The ball will be how high above the ground after 1 second?
c) How long will it take to hit the ground?
d) What is the maximum height of the ball? What time will the maximum height be attained?
 This question is from textbook College Algebra

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
I am supposing that you are at ground level.
s = -16t^2 + v0t + s0
a) What is the function that describes this problem?
Parabolic due to the square of a variable.
b) The ball will be how high above the ground after 1 second?
s = -16t^2 + v0t + s0
s = -16t^2 + 64t
s = -16(1)^2 + 64(1) = -16 + 64 = 48 feet
c) How long will it take to hit the ground?
s = -16t^2 + 64t
a=-16 and b=64 and c=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-64+%2B-+sqrt%28+64%5E2-4%2A%28-16%29%2A%280%29+%29%29%2F%282%2A%28-16%29%29+
x+=+%28-64+%2B-+sqrt%28+64%5E2+%29%29%2F%28-32%29+
x+=+%28-64+%2B-+64%29%2F%28-32%29+
x+=+%28-64+%2B+64%29%2F%28-32%29+ or x+=+%28-64+-+64%29%2F%28-32%29+
x+=+0+ or x+=+4+
After four seconds, the ball will hit the ground.
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+65%2C+-16x%5E2+%2B+64x%29+
d) What is the maximum height of the ball? What time will the maximum height be attained?
You would need to know the vertex.
s = -16t^2 + 64t
Vertex: ((-b/2a),f(x)) = ((-64/-32),f(x)) = (2,64)
The maximum height is 64 feet after 2 seconds.