Ritvik tosses a ball from where he stands on a balcony to his friend on the ground. the
height, in feet, of the ball can be represented by the function d(t) = -16° + 16+ 9,
where represents time in seconds.
part a: from what height was the ball tossed?
part b: what is the maximum height of the ball?
part c: how long does it take the ball to reach its maximum height?

Part A: Initial height is 9 feet.

Part B: Maximum height is 13 feet.

Part C: Time taken is 0.5 s.

Step-by-step explanation:

Given:

The equation to represent the height of the ball is given as:

Where, 't' is time passed in seconds.

Part A:

In order to find the initial height of the ball, the initial time must be 0 seconds.

So, plug in 0 for 't' and solve for d(0). This gives,

Therefore, the height from which the ball was tossed is 9 feet.

Part B:

The maximum height occurs when the derivative of the given equation with time is 0 as at the relative maximum, the derivative of the function is always 0.

So, differentiating the above equation with respect to time, we get:

Now, at maximum height, the derivative is 0. So,

Therefore, the maximum height is obtained by plugging in 0.5 for 't' in the height equation. This gives,

Hence, the maximum height reached by the ball is 13 ft.

Part C:

The time for which the derivative was 0 is the time taken by the ball to reach maximum height.

Therefore, from part B, the time for maximum height is 0.5 s.

each side has a different length.  

step-by-step explanation:

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