AFDA quadratic equation problem

Question

The height, h, (in feet) of a baseball that is popped up into the air is a quadratic function of the time, t, (in seconds), since it was hit. An equation that may model this situation is h(t) = 4+60t - 16t². Answer the following questions accurately, rounding to two decimal places when needed.

a. How high is the ball when it strikes the bat?

b. In how many seconds will it hit the ground?

c. At what time(s) will the ball have a height of 40 feet?

d. At what time(s) will the ball have a height of 80 feet?

e. When will the baseball reach its maximum height?

f. What is the maximum height of the ball?

Answer 1

a. This question isn't clear. First of all, the grammar is strange...please look at what you have written. What is the bag?

b.Solve the equation h(t)=0 for t.

c.Solve the equation h(t)=40.

d. Solve the equation h(t)=80.

e. The way to answer this question will depend on whether or not you have calculus yet.

The maximum point of the quadratic equation Ax² + Bx + C occurs when x=-B/2A.

f. Evaluate h(t) when t = the answer to part e.

Answer 2

When t= 0 H(0)=4. The bat was 4 feet off the ground when it hit the ball.

=For h(t)=0 we need 0 = 4+60t -16t².

For b)we can divide both sides by for and get

0 = 1+15t-4t² use the quadratic equation

zeros =( -b +-(b²-4ac)^1/2)/2a b=15, A=-4 c=1 = 15/(2*(-4)) +- ((225-(4*(-4)(1)^1/2)/8

=15/8+-((225+16)^1/2)/(-8) (225+16) =241 and 241^1/2= 15.524 so it has a height of zero at

t - 15/8 + 15.524/8 = 30.524/8 = 3.815 seconds we ignore the negative term as we can't go back in time. However, If we threw the ball back with the same tracjectory. It would travel just a little bit longer past where the bat hit the ball. It would take an extra .524/8 seconds to hit the ground.

for c and d w use the quadratic equation again. first set 40=4+60t +16t². or 10= 1+15t-4t²

or -4t²+15t-9=0 A=-4, b=15 c=-9.

Do the same for 80..

you will get a=-4 b=15 and c=-19

The apex (peak occurs at t=b/2A = 15/8..

To find the height simply plug t=15/8 into H=4 +60(t)- 16(t² =4 + 60*(15/8) - 16*(15/8)²

Hope this helps