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

The toy reaches the ground in 10 sec

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