Question

A baseball is thrown with a vertical velocity of 50 ft/s from an initial height of 6 ft. The height h in feet of the baseball can be modeled by h(t) = -16t^2 + 50t + 6, where t is the time in seconds since the ball was thrown. It takes the ball approximately _____ seconds to reach its maximum height. (Round to the nearest tenth of a second and enter only the number.)


To the nearest foot, what is the maximum height that the ball reaches? (Enter only the number.)


A player hits a foul ball with an initial vertical velocity of 70 ft/s and an initial height of 5 feet. The maximum height reached by the ball is _____ feet. (Round to the nearest foot and enter only the number.)

Answer 1

If you are not going to plot this, you can solve it by setting the derivative equal to zero. This is equivalent to finding the time when the velocity v = 50 - 32 t = 0.
That time will give you max height when put into h(t).

Answer 2

@douglaswinslowcooper can we solve it by finding the vertex of h(t) ? It is an downward parabola, so the vertex will have t = -b/2a ?

Answer 3

Sounds right and this agrees with mine.

Answer 4

hihihi, that's good.

Answer 5

I got vertex at 45 when I graphed

Answer 6

nope, it is 1.38888888888888

Answer 7

for t, hehehe

Answer 8

and 45 for h(t) but your question is finding the time, right?

Answer 9

ya

Answer 10

ok, the second part is the height

Answer 11

ok cool ya

Answer 12

height is 45 for second part and isnt 3rd part 82?