Question

If a baseball were thrown upward on the moon at 45 mph (66 feet per second) from 6 feet above the ground, its height h above the moon’s surface after t seconds would be
h(t) = -2.55t^2 + 66t + 6
a) When does the ball reach the highest point above the moon? (round to the nearest hundredth of a second)

b) What is that maximum height? (round to the nearest foot)

c) When does the ball hit the ground? (round to the nearest hundredth of a second)

d) Find h(6) and interpret what it means in a complete sentence.

Answer 1

Do you know how to figure out when it reaches its max?

Answer 2

Find the vertex x = -b/2a

Where: h(t) = at^2 + bt +c

Answer 3

I'll help you, but I'd like for you to at least take a guess at the first part.

Try graphing it on your graphing calculator or on wolfram alpha. The vertex is the highest point.

Answer 4

highest point: t= 13.010
h= 433.046
please help me out,am having a really difficult time doing this.thanks

Answer 5

a.) and b.) which I believe they're asking the same question:

t= -66/2(-2.55) = 12.94 seconds. Plug t=12.94 seconds in to your function

h(12.94) = -2.55(12.94)^2 + 66(12.94) + 6
h(12.94) = 433.059 ft

c.) The height is going to equal zero. Therefore, h(t) will equal zero.

0= -2.55t^2 + 66t + 6

You need to solve for t here. You can use the quadratic formula.

a=-2.55
b=66
c=6

http://www.mathnstuff.com/math/spoken/here/2class/320/r1.gif

t= (-66+/-sqrt(66^2-4(-2.55)(6))/(2*(-2.55))

Because of the plus/minus, you will have two solutions for t. The solution that is the lower number is not the one you want because that is when the ball started out at zero. But it started out at 6 ft. What you want is the second solution for when t=0.

t = -0.091 sec, t=25.97 sec

So when the ball HITS the ground, it will be at t=25.97 seconds. Your height will be zero. If you want to check, just try plugging 25.97 in for t and solve.


d.) h(6)=-2.55(6)^2 +66(6) + 6

h(6)= 310.2 feet

"at t=6 seconds, the ball will be 310.2 feet above the ground."

Answer 6

Since I did all of that typing, can you please try plugging this function in to your graphing calculator or wolfram alpha? Look at the vertex and try to really understand what's going on here. The highest point the ball reaches is the vertex and when the ball hits the ground, it will always be the second place where the line intersects the x-axis. Here's a good pic as an example:

http://tutorial.math.lamar.edu/Classes/Alg/Parabolas_files/image006.gif

Answer 7

"The highest point the ball reaches is the vertex and when the ball hits the ground, it will always be the second place where the line intersects the x-axis."

by line, I mean parabola lol.

Answer 8

thanks brinethery.