It will take 1.5 seconds for the grasshopper to land.
We can find this using the quadratic formula. Because the equation is in order already, we can find a, b and c as:
a = -1 (the number attached to t^2)
b = 4/3 (the number attached to t)
c = 1/4 (the number with no variable)
Then we can plug into the quadratic equation:
[tex] \frac{-b +/- \sqrt{ b^{2} -4ac } }{2a} [/tex]
[tex] \frac{-4/3 +/- \sqrt{ 4/3^{2} -4(-1)(1/4) } }{2(-1)} [/tex]
[tex] \frac{-4/3 +/- \sqrt{ 4/3^{2} + 1 } }{-2} [/tex]
1.5
