θhe height h in feet of a car above the exit ramp of an amusement park′s free-fall ride can be modled by the equation h=−16t<E> 6<E>+s where t is the time in seconds after the car drops s is the starting height of the car in feet.

Question

θhe height h in feet of a car above the exit ramp of an amusement park′s free-fall ride can be modled by the equation h=−16t<E> 6<E>+s where t is the time in seconds after the car drops s is the starting height of the car in feet.

How high above the car′s exit ramp should the ride′s designer start the drop in order for the riders to experience free-fall for at least 3 seconds?

Answer 1

I don't know what h=−16t<E> 6<E>+s is supposed to say, but I know that

h = -16t^2 is the relation between t seconds and the distance fallen in feet

Since we just want to find the distance, let's use

h = 16t^2
when t = 3
h = 16(9) = 144 feet

If this is not what you want, then correct your typing.

Answer 2

If you mean h(t) = s - 16t^2 then we need s so that

s-16*9 = 0
s = 144 ft

Answer 3

To ensure that the riders experience free-fall for at least 3 seconds, we need to find the starting height (s) of the car.

The equation given is h = -16t^2 + 6t + s.

We can plug in t = 3 into the equation to find the height (h) after 3 seconds:

h = -16(3^2) + 6(3) + s

Simplifying:

h = -16(9) + 18 + s
h = -144 + 18 + s
h = -126 + s

Since we want the height to be at least 0 at t = 3 seconds (free-fall), we can set h = 0 and solve for s:

0 = -126 + s

Rearranging the equation:

126 = s

Therefore, the starting height (s) of the car should be 126 feet above the exit ramp in order for the riders to experience free-fall for at least 3 seconds.

Answer 4

To find out how high above the car's exit ramp the ride's designer should start the drop in order for the riders to experience free-fall for at least 3 seconds, we need to set up an equation and solve for the starting height, s.

The given equation is:
h = -16t^2 + 6t + s

We know that the riders will experience free-fall for at least 3 seconds. Hence, we need to find the time at which the height, h, will be 0.

Setting h = 0 and t = 3, we can substitute these values into the equation:
0 = -16(3)^2 + 6(3) + s

Simplifying the equation:
0 = -144 + 18 + s
0 = -126 + s

Now, we need to isolate s by adding 126 to both sides of the equation:
s = 126

Therefore, the ride's designer should start the drop at a height of at least 126 feet above the car's exit ramp in order for the riders to experience free-fall for at least 3 seconds.