Question

An object is dropped from the observation deck of the Skylon Tower in Niagara Falls, Ontario. The distance, in metres, from the deck at t seconds is given by d(t)=4.9t^2

a) the height of the observation deck is 146.9 m. How fast is the object moving when it hits the ground?

The answer is 53.655 m/s.

Could someone explain how the book got 53.655 m/s.

Answer 1

First you find the time it takes to hit the ground ...
4.9t^2 = 146.9
t^2 = 29.98 sec
t = √29.98 = 5.475

if d(t) = 4.9t^2
v(t) = 9.8t

v(5.475) = 9.8(5.475) = 53.659 m/s

Since you are in calculus, I am suprised that you did not know that the derivative of distance gives you velocity.

Answer 2

It’s because this question is in unit one . We do not learn double derivatives until unit 3. So that is probably why. I had the same problem and my teacher wanted us to solve it with limits.