A ball is kicked 4 feet above the ground with an initial vertical velocity of 55 feet per second. The function h (t) = -16t^2+55t+4 represents the height h (in feet) of the ball after t seconds. Using a graph, after how many seconds is the ball 30 feet above the ground? Round your answers to the nearest tenth.

Question

Mathematics

Jennifer

30 January, 21:18

A ball is kicked 4 feet above the ground with an initial vertical velocity of 55 feet per second. The function h (t) = -16t^2+55t+4 represents the height h (in feet) of the ball after t seconds. Using a graph, after how many seconds is the ball 30 feet above the ground? Round your answers to the nearest tenth.

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Answers (1)

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Bo Moyer · Answer 1

Given:

A ball is kicked 4 feet above the ground with an initial vertical velocity of 55 feet per second.

The function represents the height h (in feet) of the ball after t seconds.

We need to determine the time of the ball at which it is 30 feet above the ground.

Time:

To determine the time that it takes for the ball to reach a height of 30 feet above the ground, let us substitute h (t) = 30, we get;

Adding both sides of the equation by 16t², we get;

Subtracting both sides of the equation by 55t, we have;

Let us solve the quadratic equation using the quadratic formula, we get;

The value of t is t = 0.6 because this denotes the time taken by the ball to reach a height of 30 feet from the ground.

Therefore, the time taken by the ball to reach a height of 30 feet above the ground is 0.6 seconds.