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+(4)/(3)t+ (1)/(4)`

When the grasshopper land on the ground,

`h(t)=0`

that is,

`-t^2+(4)/(3)t+ (1)/(4)=0`

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

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

`image`

And time cant be negative, so the correct option is

`t = (3)/(2)=1.5 seconds`

Correct option is C .