SOLUTION: Jamie is jogging along the side of the road at a constant speed of 3 m/s. When she is 30 m from a bus stop, she sees that #301 bus has its blinker on and is departing from standsti
Algebra ->
Customizable Word Problem Solvers
-> Travel
-> SOLUTION: Jamie is jogging along the side of the road at a constant speed of 3 m/s. When she is 30 m from a bus stop, she sees that #301 bus has its blinker on and is departing from standsti
Log On
Question 824204: Jamie is jogging along the side of the road at a constant speed of 3 m/s. When she is 30 m from a bus stop, she sees that #301 bus has its blinker on and is departing from standstill with the acceleration of 2 m/s2. Jamie keeps running at the same speed. The question is will she catch up with the bus and if so – how long after she notices the bus and how far from the bus stop it will happen?
You can put this solution on YOUR website! ---
position at constant acceleration:
x = (1/2)at^2 + v0t + x0
position at constant velocity:
x = vt
---
bus:
x = (1/2)at^2 + v0t + x0
v0 = 0
x0 = 30 m
a = 2 m/s^2
x = (1/2)2t^2 + 30
x = t^2 + 30
---
Jamie:
x = vt
v = 3 m/s
x = 3t
---
will Jamie catch the bus?
x = 3t = t^2 + 30
t^2 - 3t + 30 = 0
---
the above quadratic equation is in standard form, with a=1, b=-3, and c=30
---
to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 -3 30
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
---
this quadratic has two complex roots, which are:
y = 1.5 + (5.26782688)i
y = 1.5 - (5.26782688)i
the quadratic does not intercept the t-axis (the horizontal axis)
as such, there is no real-number solution to the problem
---
graph:
---
---
answer:
Jamie will not catch the bus
---
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 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
