solve the following by a quadratic equation and then solving it.

a rocket is projected vertically upwards from ground level, its height "h" meters after "t" seconds is given by the formula

h=35t-5t^2

how long does it take to reach 50 meters?

you should have two answers, explain the meaning of the two answers.

thanks

50 = 35 t - 5 t^2

5 t^2 - 35 t + 50 = 0

t^2 - 7 t + 10 = 0

(t-5)(t-2) = 0

2 on the way up and 5 on the way down

To find how long it takes for the rocket to reach 50 meters, we need to set up the equation based on the given formula and solve it using the quadratic equation.

The formula for the height of the rocket is:

h = 35t - 5t^2

We want to solve for t when the height is 50 meters. So we set up the equation:

50 = 35t - 5t^2

To make this equation easier to solve, let's rearrange it in standard quadratic form:

5t^2 - 35t + 50 = 0

Now we can use the quadratic formula to solve for t:

t = (-b ± sqrt(b^2 - 4ac)) / (2a)

For our equation, a = 5, b = -35, and c = 50.

t = (-(-35) ± sqrt((-35)^2 - 4(5)(50))) / (2(5))
t = (35 ± sqrt(1225 - 1000)) / 10
t = (35 ± sqrt(225)) / 10
t = (35 ± 15) / 10

Now we have two possible values for t:

t1 = (35 + 15) / 10 = 50 / 10 = 5
t2 = (35 - 15) / 10 = 20 / 10 = 2

Therefore, the rocket takes 2 seconds and 5 seconds to reach 50 meters.

The two answers represent two different scenarios:

1. t = 2 seconds: This is the time it takes for the rocket to reach the 50-meter height on its way up. It is the first time the rocket reaches this height.

2. t = 5 seconds: This is the time it takes for the rocket to reach the 50-meter height on its way down. It is the second time the rocket reaches this height, but this time while descending.

So, in summary, the two answers indicate the time it takes for the rocket to reach 50 meters: once while ascending and once while descending.