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%0D%0Aℎ%0D%0A=%0D%0A−%0D%0A16%0D%0A%0D%0A2%0D%0A+%0D%0A60%0D%0A%0D%0A+%0D%0A0%0D%0A , 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
To find the maximum range, we need to find the time at which the height reaches its maximum value.
The equation h = -16t^2 + 60t + 0 represents the height of the ball at time t.
To find the time at which the height is maximum, we need to find the vertex of the quadratic equation.
The vertex of a quadratic equation in the form ax^2 + bx + c is given by the formula:
x = -b/(2a)
In this case, a = -16 and b = 60.
x = -60/(2(-16))
= -60/(-32)
= 1.875
So, the maximum height is reached at 1.875 seconds.
To find the maximum range, we need to find the horizontal distance traveled when the ball is at its maximum height.
The horizontal distance traveled is given by the formula:
range = initial velocity * time
In this case, the initial velocity is 60 feet per second and the time is 1.875 seconds.
range = 60 * 1.875
= 112.5
Rounding to the nearest hundredth, the maximum range the ball will reach is approximately 112.5 feet.