A football was kicked vertically upward from a height of 4 fee...

Question

A football was kicked vertically upward from a height of 4 feet with an initial speed of 60 feet per second. The formula h=4+60t-16t² describes the ball's height above the ground, h, in feet, t seconds after it was kicked. Use this formula to solve Exercises 19–20. What was the ball's height 2 seconds after it was kicked?

Accepted Answer

Hello. Today we're going to be solving a word problem involving height. So a rocket was launched vertically upward from a platform at a height of eight ft. The initial speed of the rocket is 135 ft/s. Its height relative to the ground is defined by the equation H is equal to eight plus 100 35 t minus 16 t squared t seconds after it was launched. We need to go ahead and calculate the rockets height after four seconds. Okay, so there's two important takeaways from this word problem. The first one is that we're given an equation for height which is H is equal to eight plus 135 t minus T squared. So let's just go ahead and quickly write that down -16 T square and we are told that we want to find the rockets height after four seconds. So we want to find the rockets height when T is equal to four. So in order to solve this problem, we're going to go ahead and take this value of time and plug it directly into the equation. In terms of time. Doing that is going to give us eight plus 35 times four because we're replacing every T. In this equation with four minus 16 times four square. Alright now we just need to go ahead and simplify 135 times four is going to give me 544 squared is going to give me 16 and 16 times 16 is going to result in 256. So after multiplying what we are left with is eight plus 540 minus 256. Eight plus 540 is gonna give me 548 minus 256 is going to give me 292. And that's in terms of feet because this is the heights rocket at four seconds and this is going to be the solution to this word problem. And the answer to this word problem is going to be eight. So I hope this video helps you in understanding how to approach this type of word problem and I'll go ahead and see you all in the next video.

Key Concepts

Quadratic Functions

Substitution in Functions

Interpreting Physical Context in Algebra

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