Question

A projectile is fired upward from a tower 300 feet high with an intial velocity of 320 feet per second. Its height above ground(h feet)is given at any time(t seconds) by the equation: h=-16t²+320t+300. How many seconds will it take the projectile to reach its maximum height? What is that maximum height?

Answer 1

The projectile will take 10 seconds to reach its maximum height of 1900 feet, as calculated using the vertex formula for quadratic equations and substituting this time value back into the height equation.

Step-by-step explanation:

To determine the time it takes for the projectile to reach its maximum height, we need to find the vertex of the parabola represented by the equation h=-16t²+320t+300. The time at which a projectile reaches its maximum height in a quadratic equation like this is found using the formula t = -b/(2a), where 'a' is the coefficient of the t² term and 'b' is the coefficient of the t term. In this case, a = -16 and b = 320, so t = -320 / (2 * -16) = 10 seconds.

The maximum height is then found by substituting t back into the original equation: h = -16(10)² + 320(10) + 300 = -1600 + 3200 + 300 = 1900 feet.

Therefore, the projectile will take 10 seconds to reach its maximum height of 1900 feet.