speed is reduced by 20ft/sec every second.
So, since 50mph = 73.333 ft/sec, it will take 73.333/20 = 11/3 seconds to reduce the speed to zero
In those 11/3 seconds, the car travels 1/2 at^2 = 1/2 (20)(11/3)^2 = 134.444 ft
These kinds of problems just take a bit of thought. If there were no gravity, and no throw, the height would remain constant at
h = 450
If there were no gravity, but the stone were thrown at 8m/s, then the height would be
h = 450 - 8t
Now, tack on the acceleration due to gravity, and
h = 450 - 8t - 4.9 t^2
Solve for t when h=0
If f'(x) = 3x^3, then
f(x) = 3/4 x^4 + C
Now the line 81x+y=0 has slope -81
f'(x) = -81 when x = -3
so, the point (-3,243) is on the line
so, f(-3) = 3/4 * 81 + C = 243
C = 729/4
So, the graph of y = 3/4 x^4 + 729/4 is tangent to the line 81x+y=0 at (-3,243)
ball 1: h = 432 + 48t - 16t^2
ball 2: h = 432 + 24t - 16(t-1)^2
when is the height the same?
48t - 16t^2 = 24t - 16t^2 + 32t - 16
t = 2
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