Question

A diver begins on a platform 10 meters above the surface of the water. The diver's height is given by the equation h(t) = −4.9t^2 + 6.5t + 10, where t is the time in seconds after the diver jumps.

How many real solutions does the equation have when the diver's height is 3 m? What are they? Round to the hundredths place.

Answer 1

For this case we have the following equation:
h (t) = -4.9t ^ 2 + 6.5t + 10
Substituting the height we have:
3 = -4.9t ^ 2 + 6.5t + 10
Rewriting:
-4.9t ^ 2 + 6.5t + 10 - 3 = 0
-4.9t ^ 2 + 6.5t + 7 = 0
Which solutions are:
t1 = -0.70
t2 = 2.03
Answer:
the equation has 2 real solutions.
they are:
t1 = -0.70
t2 = 2.03