A ball is thrown vertically in the air with a velocity of...

A ball is thrown vertically in the air with a velocity of 95 ft/s. Use the projectile formula h = -16t^2 + v0t to determine at what time(s), in seconds, the ball is at a height of 120 ft. Round your answer(s) to the nearest tenth of a second.

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Transcript

00:01 Now, in this problem it says that a ball is thrown vertically in the air with velocity 90 feet per second.

00:11 Now, we have to use the projectile formula which is given by h equals to, this is given in the equation, minus 16t square plus v naught times t.

00:23 Now, we need to determine the time in seconds when the ball attains a height of 120 feet.

00:30 Okay.

00:32 So, height is 120 feet and initial speed is 90 feet per second.

00:37 You can plug it here.

00:39 So, 120 equals to minus 16t square plus v naught is 90 times t.

00:49 Here, this time t is in seconds.

00:52 Now, we can rearrange this equation.

00:54 We can take these terms to the left side.

00:57 So, what you'll get, 16t square minus 90t plus 120 is equals to zero.

01:07 Now, this is a quadratic equation and to solve t from here, we can use the quadratic formula which is given by minus b plus minus square root b square minus 4ac divided by 2a.

01:24 This formula we can use and in this case, a is 16, b is minus 90 and c is 120.

01:36 Okay.

01:37 So, just use this formula.

01:39 So, t would be equals to minus b means minus of minus 90, that is 90 plus minus square root.

01:47 B square means minus 90 whole square like this.

01:50 Minus 4 times a is 16, c is 120 divided by 2 times a...