Question 1072376: After a baseball is hit, there are two equations that can be considered. One gives the height, hopefully (in feet), the ball is above the ground t seconds after it is hit. The second is the distance, so (in feet), the ball is from home plate t seconds after it is hit. A model of this situation is given by: h=-16t^2+70t+4 and s=44.5t.
Using this model, determine whether the ball will clear a fence which is 15 feet tall and is located 325 feet from home plate.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! After a baseball is hit, there are two equations that can be considered.
One gives the height, hopefully (in feet), the ball is above the ground t seconds after it is hit.
The second is the distance, so (in feet), the ball is from home plate t seconds after it is hit.
A model of this situation is given by: h=-16t^2+70t+4 and s=44.5t.
Using this model, determine whether the ball will clear a fence which is 15 feet tall and is located 325 feet from home plate.
:
Use the height formula to find the time that the ball is at 15 ft
-16t^2 + 70t + 4 = 15
-16t^2 + 70t + 4 - 15 = 0
-16t^2 + 70t - 11 = 0
use the quadratic formula; a=-16; b=70; c=-11, I got a reasonable solution of
t = 4.2 sec
:
Using the distance equation, find how far the ball will be from home plate in 4.2 seconds
s = 44.5(4.2)
s = 187 ft, well before a distance of 385 ft, so no is the answer
:
;
We can confirm this with a graph, green line is 15'
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