A football player kicks the ball with an initial upward velocity of 60 feet per second. This situation is modeled using the equation h=−16t2+60t+0


=

16
𝑡
2
+
60
𝑡
+
0
, where h is the height in feet and t is the time in seconds. Using this equation, what is the maximum range the ball will reach? Round to the nearest hundredth.(1 point)
feet

1 answer

To find the maximum height (or range) the ball will reach using the equation h=16t2+60t+0, we need to determine the vertex of the parabola represented by this quadratic equation. The maximum height occurs at the vertex, which can be found using the formula for the time t at which the vertex occurs:

t=b2a

where a and b are coefficients from the quadratic equation h=at2+bt+c.

In this case, the coefficients are:

  • a=16
  • b=60
  • c=0

Substituting a and b into the vertex formula:

t=602(16)=6032=6032=1.875,seconds

Next, we need to find the maximum height by substituting this value of t back into the height equation:

h=16(1.875)2+60(1.875)+0

Calculating (1.875)2:

(1.875)2=3.515625

Now substitute this value back into the height equation:

h=16(3.515625)+60(1.875)

Calculating each term:

h=56.25+112.5

Now combine the terms:

h=56.25+112.5=56.25

Thus, the maximum height (or range) the ball will reach is

56.25,feet

Rounding to the nearest hundredth, the answer remains 56.25 feet.