Solve word problem

Question

A ball is dropped from a height of 100 ft above ground, and its height can be expressed as h=-16t^2+100. How long will it take

 

 

A) For the ball to reach the ground?
 B) For the ball to pass a balcony that is 36 ft above ground?

Answer 1

h = -16t² + 100

 

For time to hit the ground we have h=0 so set the equation equal to zero

 

-16t²+100 = 0

-16t²=-100

t²= 100/16

t = ±√(100/16)

t = ± 10/4 = ±2.5 seconds

 

we can discard the negative answer so t = 2.5 seconds

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For a height of 36 ft we simply set the equation equal to 36 and solve

 

-16t²+100=36

16t²=64

t²=64/16

t²=4

t = ±2 seconds

 

again, discard the negative answer so t = 2 seconds

Answer 2

we have the function:

 

h(t)=-16t^2+100

 

The time when the ball hits the ground is the value for t that makes h(t)=0...

 

solve 0=-16t^2+100 for t...thus t=\sqrt(100/16) is the time when the ball hits the ground (time moves forward so we throw away the negative \sqrt solution).

 

To solve part b) we need to find the smallest t>0 for which h(t)=36

 

so we solve 36=-16t^2+100 for t...and see that t=+/- 2, and say that it takes 2 seconds until the ball is 36 feet above the ground.  

 

Another way to see this is that for t=2, the -16t^2 has a value of -64, which means the ball has fallen 64ft from the initial height of 100ft, and thus it is even with the balcony after exactly t=2seconds.

 

Hope this helps.