A bungee jumper falls from a bridge 300 feet above ground. Her height above ground after t seconds is given by the equation h=16t^2+300 where h is the height of the jumper in feet and t is the time in seconds after she jumps. Approximately how long will it take for the bungee jumper to reach 100 feet above the ground on her initial jump?

Question

A bungee jumper falls from a bridge 300 feet above ground. Her height above ground after t seconds is given by the equation h=16t^2+300 where h is the height of the jumper in feet and t is the time in seconds after she jumps. Approximately how long will it take for the bungee jumper to reach 100 feet above the ground on her initial jump?

Answer 1

I do not think so

I think h = 300 - 16 t^2
she is accelerating DOWN

100 = 300 - 16 t^2

t^2 = 200/16

t = 10 sqrt 2 / 4 = 2.5 sqrt 2

Answer 2

To find approximately how long it will take for the bungee jumper to reach 100 feet above the ground, we need to solve the equation h = 16t^2 + 300, where h is the height and t is the time.

We want to find the time t when the height h is 100 feet. So, we replace h with 100 in the equation:

100 = 16t^2 + 300

Now we have a quadratic equation, and we can solve it by rearranging it to isolate t^2:

16t^2 = 100 - 300

16t^2 = -200

Next, we divide both sides of the equation by 16 to isolate t^2:

t^2 = -200/16

t^2 = -12.5

Since t represents time, it cannot be negative, so there is no real solution to this equation. This means that the bungee jumper will not reach a height of 100 feet above the ground on her initial jump.

It's important to note that in this case, the equation does not have a positive real solution because the given equation h = 16t^2 + 300 describes the height of the bungee jumper as a function of time during her fall. The jumper's height increases as time progresses. Therefore, it is not possible for the jumper to reach a height of 100 feet, which is lower than the starting height of 300 feet.

Answer 3

To find out how long it will take for the bungee jumper to reach 100 feet above the ground on her initial jump, we need to set up the equation h = 100 and solve for t.

The equation for the height above ground, given the time t, is h = 16t^2 + 300.

Setting h = 100, we have:
100 = 16t^2 + 300

Subtracting 300 from both sides, we get:
-200 = 16t^2

Dividing both sides by 16, we get:
-12.5 = t^2

Taking the square root of both sides, we have:
t = √(-12.5)

Since we cannot take the square root of a negative number when dealing with real numbers, it is not possible for the bungee jumper to reach 100 feet above the ground on her initial jump.