Question

The function relating the height of an object off the ground to the time spent falling is a quadratic relationship. Travis drops a
tennis ball from the top of an office building 90 meters tall. Three seconds later, the ball lands on the ground. After 2 seconds,
how far is the ball off the ground?
30 meters
40 meters
50 meters
60 meters

Answer 1

Answer: 50 meters

Step-by-step explanation: I just finished the pretest

Answer 2

Answer:  The ball is 50 m off the ground after 2 seconds

Step-by-step explanation:

Given the function relating the height of an object off the ground to the time spent falling is a quadratic relationship.

Therefore if h=height and t=time then

$h=a+bt+ct^{2}$       ----------(A)

where a,b and c are constants

Apply given conditions

At t=0s h=90 m

=> 90 m = a+0+0

=>a=90 m

Also the ball has been just dropped at t=0 s

=>$\frac{\partial h}{\partial t}=0=>\frac{\partial (a+bt+ct^{2})}{\partial t}=0$

=>$b+2ct=0$

For t=0s b = 0

Thus equation (A) is reduced to $h=90+ct^{2}$

At  t= 3 s , h=0 m

$\therefore 0= 90 +9c=>c=-10 \frac{m}{s^{2}}$

Finally we get $h=90-10t^{2}$

Therefore at t= 2.0 s , $h=(90-10\times 2^{2})m=50 m$

Thus the ball is 50 m off the ground after 2 seconds