Question

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

Answer 1

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

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

When the grasshopper land on the ground,

$h(t)=0$

that is,

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

Multiplying whole equation by 12 to get rid of denominators 3 and 4

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

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

And time cant be negative, so the correct option is

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

Correct option is C .