Question

h(t) = -2t² + 15t+8t= 30t= secondsh=meters what is the height after 3 seconds? when will the object reach a maximum height of 30 feet? (what time will the object reach its maximum height? what is the maximum height? (I'm thinking max ht is vertex.)when will the object hit the ground?

Answer 1

a) What is the height after 3 seconds?

h(t) = -2t^2 + 15t + 8

h(3) = -2(3)^2 + 15(3) + 8

h(3) = -2(9) + 45 + 8

h(3) = -18 + 45 + 8

h(3) = 35 m

b) when will the object reach a maximum height of 30 feet?

30 = -2t^2 + 15t + 8

-2t^2 + 15t + 8 - 30 = 0

-2t^2 + 15t - 22 = 0

Factor

x1 = 5.5 s x2 = 2s

There are 2 solutions

h(5.5) = -2(5.5)^2 + 15(5.5) + 8

= -60.5 + 82.5 + 8

= 30 m

h(2) = -2(2)^2 + 15(2) + 8

= -8 + 30 + 8

= 30 m

At two different times the object reach that height, 2s and 5.5 s

c) what time will the object reach its maximum height?

I'll graph the function to get the result

The time to get the maximum height it's at 4 seconds (from the graph)

d) what is the maximum height?

The maximum height it's at 36 m (from the graph)

e) when will the object hit the ground?

​At 8 seconds from the graph