the height h in feet of a ball t secons after beingtossed upward is given the formula h = 84t - 16t?

Question

how do i find h?
complete the following table of values.

t 0 1 2 3 4 5
h _ _ _ _ _ _
use the graph to find a positive root of the equqtion 0 = 84t - 16t^2
after how many seconds will the ball hit the ground?

Answer 1

It's plug 'n play ☺
t = 0 so h = 84*0-16*0 = 0
t = 1 so h = 84*1 - 16*1 = 68

Now go get hot on your calculator.

But first, check that equation. It just doesn't look right ☺


Doug

Answer 2

I think you meant: h = 84t-16t^2

Just plug t = 0,1,2,3,4,5 into this equation and you will get h = 0,68,104,108,80,20 feet respectively. This gives you your six graph points. You can plot them and see when h will be zero again.
This can also be computed exactly by solving the equation
0 = 84t - 16t^2 = t(84-16t). This equation holds when t=0 and when 84-16t =0 which is true when t = 84/16 = 5.25 sec.

(Note, this is the standard physics equation: d = v t + 1/2 a t^2 ; where d = distance, v = velocity and a = acceleration. In the case of a ball thrown upward at the earth's surface, a = -32 ft /sec^2 and if the ball is thrown with an upward velocity of 84 ft/sec, then the height(h) in feet is given by h = 84t - 16t^2)

Answer 3

h = 84t - 16t^2

h = 84(0) - 16(0)^2 = 0 - 0 = 0
h = 84(1) - 16(1)^2 = 84 - 16 = 68
h = 84(2) - 16(2)^2 = 168 - 16(4) = 168 - 64 = 104
h = 84(3) - 16(3)^2 = 252 - 16(9) = 252 - 144 = 108
h = 84(4) - 16(4)^2 = 336 - 16(16) = 336 - 256 = 80
h = 84(5) - 16(5)^2 = 420 - 16(25) = 420 - 400 = 20

ANS :
(0,0), (1,68), (2,104), (3,108), (4,80), (5,20)

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0 = 84t - 16t^2
-16t^2 + 84t = 0
16t^2 - 84t = 0
4t(4t - 21) = 0
4t - 21 = 0
4t = 21
t = (21/4)
t = 5.25

ANS : 5.25 seconds