So I have this question that I have no idea how to approach, it was one of my math problems that belong in the category of factoring general quadratics, but I didn't know how to factor it: The equation y=−4.9t2+42t+18.9 describes the height (in meters) of a ball tossed up in the air at 42 meters per second from a height of 18.9 meters from the ground, as a function of time in seconds. In how many seconds will the ball hit the ground?
So I have this question that I have no idea how to approach,
it was one of my math problems that belong in the category of factoring general quadratics,
but I didn't know how to factor it:
The equation
y=−4.9t2+42t+18.9
describes the height (in meters) of a ball tossed up in the air at 42 meters per second from a height of 18.9 meters from the ground,
as a function of time in seconds.
In how many seconds will the ball hit the ground?
Hit the ground means y=0 !
−4.9t2+42t+18.9=0|⋅(−1)4.9t2−42t−18.9=0t=42±√422−4⋅4.9⋅(−18.9)2⋅4.9t=42±√422+370.449.8t=42±√1764+370.449.8t=42±√2134.449.8t=42±46.29.8|t>0 !t=42+46.29.8t=88.29.8t=9 seconds
In 9 seconds the ball will hit the ground.