SOLUTION: Michael throws a baseball into the air with an initial vertical velocity of 180 feet per second from a 100 foot cliff. A: Write the height of the baseball as a function of time.

Question 825435: Michael throws a baseball into the air with an initial vertical velocity of 180 feet per second from a 100 foot cliff.
A: Write the height of the baseball as a function of time.
B: When will the baseball be 200 feet high?
C: When will the baseball reach its maximum height?
D: How high is the baseball after 3 seconds?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
---
equation of ballistic motion:
y(t) = (1/2)gt^2 + v0t + y0
---
where y(t) is height at time t
g = acceleration due to gravity
v0 = initial velocity
y0 = initial height
t = time
---
y(t) = (1/2)-32t^2 + 180t + 100
---
answer A:
y(t) = -16t^2 + 180t + 100
---
setup for B:
200 = -16t^2 + 180t + 100
-16t^2 + 180t - 100 = 0
---
the above quadratic equation is in standard form, with a=-16, b=180, and c=-100
---
to solve the quadratic equation, by using the quadratic formula, copy and paste this:
-16 180 -100
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
---
the quadratic has two real roots at:
t = 0.586088907
t = 10.6639111
---
the quadratic vertex is a maximum at: ( t= 5.625, y(t)= 406.25 )
---
answer B:
the ball is at 200 feet twice:
t = 0.586088907 seconds
t = 10.6639111 seconds
---
answer C:
at t= 5.625 seconds the ball reaches its maximum height of 406.25 feet
---
answer D:
y(3) = -16*3^2 + 180*3 + 100
y(3) = 496 feet
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 4-equations 4-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
RELATED QUESTIONS
A baseball player hits a baseball into the air from a height of 3 feet with an initial... (answered by ankor@dixie-net.com)

Solve rounding the answers to the nearest hundredth. 1. A javelin thrower releases a... (answered by ikleyn)

One football is kicked into the air with an initial vertical velocity of 44 feet per... (answered by ankor@dixie-net.com)

Use the verticle height formula to solve the following h= -16t^ + intitial velocity +... (answered by ankor@dixie-net.com)

A rocket is launched from atop a 101 foot cliff with an initial velocity of 116 feet per... (answered by Boreal)

Thank you! You hit a baseball straight into the air. The baseball is hit with an initial... (answered by ankor@dixie-net.com)

A dog leaps into the air with an initial vertical velocity of 12 feet per second. How... (answered by ikleyn)

Baseball Tonisha hit a baseball into the air with an initial upward velocity of 48... (answered by jim_thompson5910)

An astronaut on Mars throws a ball into the air with an initial velocity of 30 feet per (answered by ikleyn,jorel1380)