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

Question

, 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)

Answer 1

To find the maximum height (or the apex) that the ball reaches, we can use the vertex formula for a parabola given by the equation $h=-16t^2+60t+0$. The general formula for the time $t$ at which the maximum height occurs in a quadratic equation $a{x}^2+bx+c$ is given by:

$$t=-\frac{b}{2a}$$

In this case, $a=-16$ and $b=60$. Plugging in the values:

$$t=-\frac{60}{2(-16)}=\frac{60}{32}=1.875\text{ seconds}$$

Next, we substitute $t=1.875$ back into the height equation to find the maximum height:

$$h=-16(1.875{)}^2+60(1.875)+0$$

Calculating $(1.875{)}^2$:

$$(1.875{)}^2=3.515625$$

Now, substituting this value into the equation:

$$h=-16(3.515625)+60(1.875)$$

Calculating each term:

$$-16(3.515625)=-56.25$$ $$60(1.875)=112.5$$

Combining the terms:

$$h=-56.25+112.5=56.25$$

Thus, the maximum height the ball will reach is 56.25 feet.