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The equation  y=-16t^2 +80t describes the height (in feet) of a projectile launched from the ground at 80 feet per second. At what  t will the projectile reach 36 feet in height for the first time? Express your answer as a decimal rounded to the nearest tenth.

 Aug 2, 2023
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The equation  y=-16t^2 +80t describes the height (in feet) of a projectile launched from the ground at 80 feet per second. At what  t will the projectile reach 36 feet in height for the first time? Express your answer as a decimal rounded to the nearest tenth.    

 

y  =  –16t2 + 80t describes the height, so let's just set y to the desired height and see what happens.   

 

                                                                  36  =  –16t2 + 80t      

 

Subtract 36 from both sides.                       0  =  –16t2 + 80t – 36   

 

Multiply both sides by –1.                         16t2 – 80t + 36  =  0  

 

Divide both sides by 4, to get     

more manageable coefficients.                   4t2 – 20t + 9  =  0   

 

Factor.                                                        (2t – 1)(2t – 9)  =  0    

 

                                                                    2t  =  1      ----->  t  =  0.5 sec   

                                                            and  2t  =  9      ----->  t  =  4.5 sec   

 

The problem asks for the time  

to get to 36 feet on the way up,       

so it's the smaller answer.   

 

check answer    

                                                          y  =  –16t2 + 80t    

                                                          y  =  –(16 • 0.25) + (80 • 0.5)    

                                                          y  =  –4 + 40    

                                                          y  =  36       

.

 Aug 2, 2023

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