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hjlf
3 years ago
9

A projectile is fired vertically upward, and its height s(t) in feet after t seconds is given by the function s(t)=-16t^2+600t+8

00. After how many seconds, to the nearest tenth, will the projectile hit the ground?
Mathematics
1 answer:
nalin [4]3 years ago
8 0

Answer:

The projectile will hit the ground after 38.8 seconds.

Step-by-step explanation:

You know that the height s (t) in feet of the projectile after t seconds is given by the function

s(t) = - 16t² + 600t + 800.

To know the time at which the projectile will hit the ground, you must replace s(t) by height 0:

0=- 16t² + 600t + 800

This is a quadratic function of the form ax2 + bx + c, where a= -16, b=600 and c=800.

To solve a quadratic function, you must apply the expression:

x1,x2=\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}

In this case:

x1,x2=\frac{-600+-\sqrt{600^{2}-4*(-16)*800 } }{2*(-16)}

Solving:

x1,x2=\frac{-600+-\sqrt{360000+51200 } }{-32}

x1,x2=\frac{-600+-\sqrt{411200 } }{-32}

x1,x2=\frac{-600+-641.25 }{-32}

So:

x1=\frac{-600+641.25 }{-32}

x1=\frac{41.25 }{-32}

x1= -1.289 seconds

and

x2=\frac{-600-641.25 }{-32}

x2=\frac{-1241.25 }{-32}

x2= 38.789 ≅ 38.8 seconds

Time cannot be negative. So, <u><em>the projectile will hit the ground after 38.8 seconds.</em></u>

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