Ouadratic Equations and Functions
Solving a word problem using a quadratic equation with irrational roots
A ball is thrown from a height of 64 meters with an initial downward velocity of $3 m / s$ . The ball's height $h$ (in meters) after $t$ seconds is given by the following
$h = 64 - 3 t - 5 t^{2}$

How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
$t = ◻ seconds$
$◻ \propto ◻$

Answer

Expert–verified

Hide Steps

Answer

Final Answer: $3.29$ seconds.

Steps

Step 1 ：The problem gives us a quadratic equation in the form of $a x^{2} + b x + c = 0$ . We can solve this equation using the quadratic formula $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ . In this case, a = -5, b = -3, and c = 64. We will substitute these values into the quadratic formula to find the value of 't'.

Step 2 ：Substituting the values into the quadratic formula, we get two solutions for 't': 3.29 and -3.89. However, time cannot be negative, so we discard the negative solution.

Step 3 ：The ball hits the ground 3.29 seconds after it is thrown.

Step 4 ：Final Answer: $3.29$ seconds.

Answer

Popular Problems