Question

a rock is thrown at the top of a 30-foot cliff with an initial of 29 feet per second. the formula for the height H of a projectile after time t is given by H = - 1/2 gt^2 + tv + h, where g is the acceleration due to gravity, which on earth is 32 feet per second squared in U.S. customary units, v is the initial velocity, and h is the object’s starting height above ground. what is the maximum height of the rock? enter the answer rounded to the nearest whole foot

Answer 1

43 ft

Explanation:

You want to know the maximum height of a rock whose height is given by the equation H = -16t² +29t +30.

Height

One way to find the maximum height is to rewrite the height function to vertex form.

H = -16(t² -29/16t) +30

H = -16(t² -29/16t +(29/32)²) +30 +16(29/32)²

The last two terms sum to the maximum height:

Hmax = 30 +16(29/32)^2 = 43 9/64

The maximum height is about 43 feet.

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Additional comment

The finished vertex form equation is ...

H = -16(t -29/32)² +43 9/64

This tells us the maximum height occurred when t=29/32.