Question

On Mars, if you hit a baseball, the height f the ball a time t would be modeled by the quadratic function h(t) += -1.85t^2+20t+1 is in seconds and h(t) is in meters a) when will the ball hit the ground?

b) how long will the ball be above 17m?

Answer 1

The ball will hit the ground when h(t)=0 so

-1.85t^2+20t+1=0 using the quadratic formula for simplicity...

t=(-20±√407.4)/-3.7, since t>0

t=(-20-√407.4)/-3.7 seconds

t≈10.86 seconds (to nearest hundredth of a second)

....

How long will the ball be greater than 17m, h(t)>17

-1.85t^2+20t+1>17

-1.85t^2+20t-16>0

t>(-20+√281.6)/-3.7

t<(-20-√281.6)/-3.7 approximately...

t<9.94

t>0.87

0.87<t<9.94 to the nearest hundredth of a second

0.88≤t≤9.93

9.93-0.88=9.05

So the ball will be greater than 17m for about 9.05 seconds.