Sam is on the diving team at his school. The pallway of his dive into the pool is represented by the equation below.
A. Find the highest point of Sam's dive.
B find the time it will take to get to the highest point of Sam's dive.
H=-16t^2+15t+10
H= height if feet
T= time in seconds
A. To find the highest point of Sam's dive, we need to find the vertex of the quadratic equation H=-16t^2+15t+10. The equation for the vertex of a parabola in the form of y=ax^2+bx+c is given by x=-b/(2a). In this case, a=-16 and b=15.
So, x = -15/(2*-16) = -15/-32 = 15/32
Now, plug in t=15/32 into the equation to find the highest point:
H = -16(15/32)^2 + 15(15/32) + 10
= -16(225/1024) + 225/32 + 10
= -3600/1024 + 225/32 + 10
= -225/64 + 225/32 + 10
= -225/64 + 450/64 + 640/64
= 865/64
Therefore, the highest point of Sam's dive is at a height of 865/64 feet.
B. To find the time it will take to get to the highest point of Sam's dive, we already found that the time to reach the highest point is t=15/32 seconds.