Henry is standing on a bridge over a creek. If he could throw a stone straight up into the air with a velocity of 50 feet per second, could the stone reach a height of 60 feet above the creek? He is 20 feet from the water

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 releasedV₀ = the object's speed when it was released, negtive if downwardA = the object's acceleration, negative if downwardt = time since the object was releasedIn the case that involves Henry on the bridge . . .H₀ = 0V₀ = +50 ft/secA = -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 + 16t²Subtract 40 from each side:16t² + 50t - 40 = 0Just to make the numbers more manageable, divide each side by 2 :8t² + 25t - 20 = 0Plug 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, andsince it's negative, our equation has no real solutions ... there's nosuch 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.Whew!===============================================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. That's pretty close, but not quite 40 feet above Henry.So the answer to the question is:  No.

Balance the energy=K.E.=P.E(at the max height)1/2mv^2=mghm cancels out,or, h=1/2v^2/gor, h=1/2*50*50/32or, 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.