Question

For the equation 40=40−10t−5t². Which represents the height (h) of a ball as a function of time (t) when it's thrown, when is the ball on the ground (i.e., h = 0)?

Answer 1

The ball hits the ground when the height is zero, which for the provided quadratic equation occurs at t = 0 seconds, as time cannot be negative.

Step-by-step explanation:

To determine when the ball is on the ground, we need to find when the height (h) equals zero in the equation 40 = 40 - 10t - 5t2. This represents a quadratic equation, which is in standard form 0 = -10t - 5t2. We can solve for t using the quadratic formula or by factoring if possible.

To solve this particular quadratic equation, we first rewrite it as 0 = -5t2 - 10t. Factoring out the common factor of -5t, we get 0 = -5t(t + 2). Setting each factor equal to zero gives us t = 0 or t = -2. Since time cannot be negative, we dismiss t = -2 and determine that the ball hits the ground at t = 0 seconds, which is the moment it is thrown.