Question

100 POINTS !! The trajectory of a potato launched from a potato cannon on the ground at an angle of 45 degrees with an initial speed of 70 meters per second can be modeled by the parabola f(x) = x − 0.002x2, where the x-axis is the ground. Find the height of the highest point of the trajectory and the horizontal distance the potato travels before hitting the ground. A.height: 125 m; distance: 500 m B.height: 250 m; distance: 22 m C. height: 500 m; distance: 125 m D. height: 22 m; distance: 250 m

Answer 1

`\\ \rm\rightarrowtail y=x-0.002x^2`

So

• Put 250

`\\ \rm\rightarrowtail y=250-0.002(250)^2`

`\\ \rm\rightarrowtail y=250-0.002(62500)`

`\\ \rm\rightarrowtail y=250-125`

`\\ \rm\rightarrowtail y=125m`

• This is max height

Distance:-

• 2×height
• 2×125
• 500m

Answer 2

height: 125m; distance: 500m

Explanation:

x = 250

f(x) = x − 0.002x2

f(x) = 250 − 0.002(250 )2

= 250 − 0.002(62,500)

= 250 − 125

= 125

250 times 2 = 500