Question

The height after t seconds of an object projected upward with an initial velocity of 48 feet per second from a 210-foot tower can be modeled by h=−16t^2 + 48t +210. The height of a neighboring 50-foot tall building is modeled by the equation h=50. The time (t) when the object will be at the same height as the building is found to be t = –2 and t = 5. Which statement BEST describes the validity of these solutions? A. Neither solution is valid since time values cannot be squared. B. The solution t = – 2 is the only solution since 5 seconds is an unreasonable amount of time for the object to reach a height of 50 feet. C. The solution t = 5 is the only valid solution to this system since time cannot be negative. D. Both are valid solutions to this system since both values make the equation h=−16t^2+ 48t + 210 true.

Answer 1

Given:

The height h of an object after t seconds is

$h=-16t^2+48t+210$

The height of a neighboring 50-foot tall building is modeled by the equation h=50.

The time (t) when the object will be at the same height as the building is found to be t = –2 and t = 5.

To find:

The statement which describes the validity of these solutions.

Solution:

We have,

$h=-16t^2+48t+210$

Here, t is the time in seconds.

For t=-2,

$h=-16(2)^2+48(-2)+210$

$h=-64-96+210$

$h=50$

For t=5,

$h=-16(5)^2+48(5)+210$

$h=-400+240+210$

$h=50$

So, the value of h is 50 at t=-2 and t=5.

We know that time is always positive so it cannot be negative value. It means t=-2 is not possible.

The solution t = 5 is the only valid solution to this system since time cannot be negative.

Therefore, the correct option is C.