Supreme Scream is a ride in which passengers are dropped and experience the acce

Question

Supreme Scream is a ride in which passengers are dropped and experience the acceleration of gravity, before being rapidly brought to a complete stop. The ride reaches a height of 76.8 meters. An object falling under the force of gravity has height modeled by the equation H(t)4.9t2+vt+h, where H is measured in meters, v is the initial velocity in meters/second, and h is the initial height in meters. (a) Keeping in mind that the ride drops passengers from a stop, write a function equation to model the height of passengers as a function of time since the ride started. is the free fall portion of the ride? fast are passengers traveling at the moment when the brakes are first applied? (b) If riders are allowed to free fall for 10 meters before the brakes are applied, how long (in seconds) (c) If the speed of passengers on the ride is given by the equation S(t)-9.8t (meters/second), how

Explanation / Answer

a) v = 0
h = 76.8

So, H(t) = -4.9t^2 + 76.8 -----> ANS

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b)
When they freefall for 10 m
they are at 66.8 m above grnd

So, 66.8 = -4.9t^2 + 76.8

So, 4.9t^2 = 10

t = 10/7 seconds

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c)
When brakes are applied
they are movin at
9.8 * 10/7

98/7

14 meter per sec

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d)
80 miles per hr

We given that 1 m/s = 2.24 miles per hr
So, x m/s = 80 miles per hr

Forming fractions, we get :
1/x = 2.24/80

Crossmultiply :
2.24x = 80

x = 80/2.24

x = 250/7 m/s

So, we have
250/7 = 9.8*t

t = (250/7) / 9.8

t = 3.6443148688046647 seconds to free fall

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