A grasshopper jumps off a tree stump. The height, in feet, of the grasshopper above the ground after t seconds is modeled by the

Question

kondor19780726

1 month ago

10

A grasshopper jumps off a tree stump. The height, in feet, of the grasshopper above the ground after t seconds is modeled by the

function shown below. After how many seconds will the grasshopper land on the ground? Round to the nearest tenth.
h(t) = -t^2 + 4/3t + 1/4

A. -0.2 seconds
B. 0.5 seconds
C. 1.5 seconds
D. 0.7 seconds

Mathematics

1 answer:

zzz [12.3K] · Answer 1 · 2026-03-05T18:00:52+03:00

The height in feet of the grasshopper above the ground after t seconds can be described by the function, which is

$h(t) =-t^2+\frac{4}{3}t+ \frac{1}{4}$

When the grasshopper reaches the ground,

$h(t)=0$

that is,

$-t^2+\frac{4}{3}t+ \frac{1}{4}=0$

Multiplying the entire equation by 12 to eliminate the denominators of 3 and 4

$-12t^2+16t +3=0$

$(3-2t)(6t+1)=0 \\ 3-2t=0, 6t+1=0 \\ t= \frac{3}{2}, \frac{-1}{6}$

Moreover, time cannot be negative, therefore the accurate answer is

$t = \frac{3}{2}=1.5 seconds$

The correct option is C.