PRACTICE IT Use the worked example above to help you solve this problem. A stone

Question

PRACTICE IT Use the worked example above to help you solve this problem. A stone is thrown from the top of a building with an initial velocity of 22.3 m/s straight upward, at an initial height of 52.0 m above the ground. The stone just misses the edge of the roof on its way down, as shown in the figure. (a) Determine the time needed for the stone to reach its maximum height. 2.27 (b) Determine the maximum height. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m (c) Determine the time needed for the stone to return to the height from which it was thrown, and the velocity of the stone at that instant. Time Velocity (d) Determine the time needed for the stone to reach the ground. (e) Determine the velocity and position of the stone at6.13 s. Velocity Position m/s

Explanation / Answer

b) maximum height from building = u2 /2g = 22.32 / 2*9.8 = 25.4 m

maximum height from ground is 52+25.4 = 77.4 m

c) time needed = 2*u /g = 2*22.3/9.8 = 4.55 s

in this half time is for going upward and half is for coming downward.

so time taken in coming downward = 4.55/2 = 2.275 s

at top point , initial velocity u is zero.

so v = u+g*t = 9.8*2.275 = 22.295 m/s

d) time taken in coming down from maximum height to ground = (2*h/g)1/2 = (2*77.4/9.8)1/2 = 3.97 second.

so total time taken = time in going upward+time in coming downward to the ground = 2.27+3.97 = 6.24 s

e ) out of 6.13 s , 2.27 s will be in going upward.so time taken in only coming downward is 6.13-2.27 = 3.86 s.

so we now take only downward motion from maximum height for which initial velocity u is zero.

so v = u+g*t = 0 + 9.8 *3.86 = 37.8m/s

position h = u*t +1/2*g*t2 = 0+ 0.5*9.8*3.862 = 73 m

this is the position from maximum height attained by stone i.e 77.4 m. so position from ground is 77.4-73 = 4.4 m

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.