Question

Canada’s Wonderland has a roller coaster named ‘Leviathan’. It boasts a maximum height of 93 m, 80⁰ drop, speeds of 148 kms and is 1673m long. At its maximum height Mr. Currie drops his gum from his mouth. The height of the gum can be given by the mathematical model:

h = 93 - 4.9t2, where t is in seconds and h is measured in metres.

a) Find the average velocity of the gum on the intervals 2<t<3 and 2<t<2.1

b) Find the instantaneous velocity when t = 1.5.

Answer 1

I got dizzy watching the video of the ride. Never mind the ride!

(a) average velocity
- t∈(2,3)
Average velocity = v(final)-v(initial)
=(93-4.9(3²)) - (93-4.9(2²)
=4.9(9-4)
=24.5 m/s
- t∈(2,2.1)
similar to above.

(b)
h(t)=93-4.9t²
instantaneous velocity at time t
v(t)=h'(t)
=-9.8t
At t=1.5
v(t)=h'(t)=-9.8*1.5=14.7 m/s