Balance the energy=
K. E. =P. E(at the max height)
m cancels out,
or, h=39 ft (approx. )
As he is 20 ft above water so total height the stone an reach 39+20=59 ft.
Hence, it cant reach 60 ft over the creek.
Henry is 20 feet above the water. You want to know whether stone can reach
60 feet above the water. So what youre really asking is: Calculate whether
the stone can reach 40 feet above Henry, and we can forget about the creek?
Call Henrys elevation zero, and the height of the stone at any time after
the toss H.
Way back among the pages in your Physics book that are clean and shiny
because they have never yet been exposed to air or sunlight, you will find
the formula for the height of an object in free-fall:
Height = H₀ + V₀t + 1/2 A t²
H₀ = the objects height when it was released
V₀ = the objects speed when it was released, negtive if downward
A = the objects acceleration, negative if downward
t = time since the object was released
In the case that involves Henry on the bridge.
H₀ = 0
V₀ = +50 ft/sec
A = -32 ft/sec² (acceleration due to gravity)
We want to know if the height of the object can ever be +40 feet.
We can plug all the numbers into the equation, and solve it. Since the equation
is written in terms of t , any solution we get will be a time. Thats not what
were looking for, but if theres any real solution, then well know that its possible.
40 = 50t + 16t²
Subtract 40 from each side:
16t² + 50t - 40 = 0
Just to make the numbers more manageable, divide each side by 2 :
8t² + 25t - 20 = 0
Plug this into the quadratic formula:
t = (1/16) x (-25 plus or minus the square root of [625 - 640] )
Do you see that square root of -15 in there?
The -15 is called the discriminant of our quadratic equation, and
since its negative, our equation has no real solutions. theres no
such thing as the real square root of a negative number.
So the answer to the question is: No. The stone never reaches a height
of 40 feet above Henry, or 60 feet above the creek.
A slightly easier way to do it:
Henry throws the stone upward at 50 ft/sec.
The acceleration of gravity is 32 ft/sec² downward.
The stone keeps rising for (50/32) = 1.5625 second, until its upward speed
has shrunk to zero, and then it starts falling.
How high is it when it stops rising?
Its upward speed was 50 when Henry tossed it, and zero when it stopped rising.
Its average speed on the way up was (1/2)(50 + 0) = 25 ft/sec upward.
It has that average speed for 1.5625 seconds.
How far does it climb in that time?
H = (25 ft/sec) x (1.5625 sec) = 39.0625 feet.
Thats pretty close, but not quite 40 feet above Henry.
So the answer to the question is: No.