Question

A trampolinist steps off from 15 feet above ground to a trampoline 13 feet below. The function h (t) = -16 t 2 + 15, where t represents the time in seconds, gives the height h, in feet, of the trampolinist above the ground as he falls. When will the trampolinist land on the trampoline?

Answer 1

Answer:

Trampolinist will land on the trampoline after 0.9 seconds.

Step-by-step explanation:

The function h(t) = -16t² + 15 represents the relation between height 'h' above the ground and the time 't' of the trampolinist.

We have to find the time when trampolinist lands on the ground.

That means we have to find the value of 't' when h(t) = 15 - 13 = 2

[Since trampoline is 2 feet above the ground]

When we plug in the value h(t) = 2

2 = -16t² + 15

2 + 16t² = -16t² + 16t² + 15

16t² + 2 = 15

16t² + 2 - 2 = 15 - 2

16t² = 13

$\frac{16t^{2}}{16}=\frac{13}{16}$

$t^{2}=\frac{13}{16}$

t = $\sqrt{\frac{13}{16}}$

t ≈ 0.9 seconds

Therefore, trampolinist will land on the trampoline at 0.9 seconds.