The height of a new building will be 951 ft

Question

The height of a new building will be 951 ft. Neglecting air resistance, the height of an object dropped from this building a time T seconds would be given by the polynomial H(T)= -16T^2+951.

 

a) find the height of the object at tome T=4 seconds

b)at what time will the object pass by a window washer that is 450 ft. high?

Answer 1

H(t) is a function. It is the relationship between height of the object and time from when the object is dropped. At time = 0 (before the object begins to fall), the height is 951 feet which is the height of the building because the object is dropped from the top of the building. The height of the object at any other time can be calculated using the equation for the function which is given in the question.

 

H(t) = height of the object = -16T² + 951

 

Notice if you plug in the number zero for time T, you get height  = 951 which is what you expect.

 

So to answer part a, you plug in the value 4

 

In part b, you are given the height of the object and asked to find the time that has passed since the object was dropped. You use the same equation but now you plug in 450 for height and solve for time. So it is just the other way around.

 

at t= 4, H = -16(4)² + 951

 

at H = 450, 450 = -16T² + 951