Question

The quadratic function h(t) = −4.9t^2 + 50t + 2 represents the height, in meters, of a toy rocket t seconds after launch. How many seconds will it take the toy to reach the ground? State your answer to the nearest whole second.

Answer 1

It reaches the ground in 10 sec

Answer 2

Answer:

The toy reaches the ground in 10 sec

Step-by-step explanation:

When the rocket hits the ground, h becomes zero (0).  Thus, our problem here is to solve the equation h(t) = −4.9t^2 + 50t + 2 = 0,

Because of the fractional coefficient -4.9, it's best to use the quadratic equation here.  The coefficients of the t terms are {-4.9, 50, 2}.  Thus,

the discriminant is b^2 - 4ac  = 50² - 4(-4.9)(2) = 2539.2, and the square root of this is 50.39.

The quadratic formula is as follows:

      -b ± √discriminant

t = -------------------------------

                 2a

which here is:

      -50 ± 50.39

t = ------------------------      Since t represents time, only the positive result

               -9.8                 is relevant here; it is 10.24 sec,

which rounds off to 10 sec

The toy reaches the ground in 10 sec