Henry is 20 feet above the water. You want to know whether stone can reach 60 feet above the water. So what you're really asking is: Calculate whether the stone can reach 40 feet above Henry, and we can forget about the creek ?
Call Henry's 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 object's height when it was released V₀ = the object's speed when it was released, negtive if downward A = the object's 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'. That's not what we're looking for, but if there's any real solution, then we'll know that it's 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 it's negative, our equation has no real solutions ... there's no such thing as the real square root of a negative number.
So the answer to the question is: <u>No</u>. The stone never reaches a height of 40 feet above Henry, or 60 feet above the creek.
Balance the energy= K.E.=P.E(at the max height) 1/2mv^2=mgh m cancels out, or, h=1/2v^2/g or, h=1/2*50*50/32 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 can't reach 60 ft over the creek.
1 and 1/6 is the correct answer because 4/1 multiplied by 1/3 is 4/3. 4/3 multiplied by 7/8 is 28/24 or 1 and 4/24, which can be simplified down to 1 and 1/6.