The height in feet reached by a baseball tossed upward at a speet of 48 ft/second from the ground is given by h(t)=-16t^2+48t, where t represents time in seconds after the ball is tossed. at what time does the baseball reach 24ft? use the quadratic formula... ok I know this can be solve using the vertex...right? how do you solve it?

Question

anonymous · Answer

The LHS of the equation is your height. If you want to calculate t for a given height, write:
24 = -16t^2 + 48t. And solve the quadratic equation using the quadratic formula. The negative solution does not make physical sense, so pick the positive one.

campbell_st · Answer

equate the information

then  24 = -16t^2 + 48t  

then 16t^2 - 48t + 24 = 0

or  8(2t^2 - 6t + 3) = 0 

you need to solve for t  

 there will be 2 time values as the path is parabolic... there will be a time going up and going down

you need the general quadratic formula to show

$$t = (6 \pm2\sqrt{3})4$$

campbell_st · Answer

oops $$t = (6 \pm 2\sqrt{3})/4$$

anonymous · Answer

Just a remark: when I said the negative solution does not make physical sense what I meant is that if you end up with a negative value for time, that doesn't make that much of a sense. In this problem, both must be positive because you pass at h = 24ft two times: going up and going down.

anonymous · Answer

|dw:1335058395091:dw|what if do this...would it be wrong?

campbell_st · Answer

thats the axis if symmetry of the curve and the vertex of the curve lies on that line

campbell_st · Answer

but the vertex won't help in solving the problem other than letting you know there is a value for t either side of t = 3/2

anonymous · Answer

oh ok i get it it would just give me the height not the time..