Question

The function h(t)=-16t^2+vt+10 The height of a platform diver above the water in feet T seconds after the diver leaves a platform with an initial velocity V in feet per second. What is the initial velocity

Answer 1

To find the initial velocity of the platform diver, we can set the height function equal to zero and solve for the variable representing the initial velocity in the quadratic equation.

Step-by-step explanation:

The given function representing the height of the platform diver above the water is h(t) = -16t^2 + vt + 10, where h(t) is the height in feet, t is the time in seconds, and v is the initial velocity in feet per second. To find the initial velocity, we can use the fact that when the diver leaves the platform, the height is 0, so we set h(t) = 0 and solve for v.

0 = -16t^2 + vt + 10

By solving this quadratic equation, we can find the value of v, which represents the initial velocity of the platform diver.

Answer 2

The initial velocity 'v' is the coefficient of the 't' term in the quadratic function h(t). At t=0, the equation simplifies, and 'v' is the initial velocity with which the diver left the platform.

Step-by-step explanation:

The student's question deals with a quadratic equation representing the height of a platform diver above the water as a function of time, h(t) = -16t^2 + vt + 10. Here, initial velocity 'v' is the coefficient of the linear term 't' in the equation. To find the initial velocity, we look at the equation at the moment the diver leaves the platform, which is when t = 0. At this instant, the only term that affects the height is the constant term 10 feet, which represents the height of the platform above the water. However, since we have to find the velocity 'v', we look at the term vt in the equation. The initial velocity is the velocity of the diver at the moment of the leap (t = 0), which is the value of 'v' because the height h(0) = -16(0)^2 + v(0) + 10 simplifies to 10 feet, the height of the platform, with no influence from the velocity term at that specific moment.