Question

A bullet is shot vertically upward with an initial velocity of 128 ft/s. The bullet's height after t seconds is y(t) = 128t - 16t2. What is the height of the bullet at the time the velocity is 0 ft/s?

Answer 1

The height of the bullet when the velocity is zero is 256 ft.

Height of the bullet when the velocity is zero

The height of the bullet when the velocity is zero is determined by taking derivative of the function as shown below;

$v = \frac{dy}{dt} = 128 -32t \\\\when \ v \ is \ zero\\\\v = 0\\\\128 - 32t = 0\\\\32t = 128\\\\t = \frac{128}{32} \\\\t = 4 \ s$

The height of the bullet at this time is calculated as follows;

$y(4) = 128(4) - 16(4)^2\\\\y(4) = 256 \ ft$

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