A stone is thrown vertically upward with a speed of 24 m/s?

Question

A) How fast is it moving when it is at a height of 13m.B) How much time is required to reach this heightC) Why are there two answers to (B)

Hermina Ferry · Accepted Answer

Since the stone is thrown upward, its acceleration is -9.8 m/s^2. Let’s use the following equation to determine its velocity at this height. vf^2= vi^2 + 2 a d, a = -9.8vf^2 = 24^2 + 2 -9.8 13vf = ± √321.2This is approximately ±17.9 m/s. Since the ball is rising, its velocity is positive. Let’s use the following equation to determine the time.vf = vi – a * t√321.2 = 24 – 9.8 * tt = (24 – √321.2) ÷ 9.8This is approximately 0.62 seconds. The next time the stone is at this height, its velocity is -√321.2.Let’s use the same equation to determine the time.-√321.2 = 24 – 9.8 * tt = (√321.2 + 24) ÷ 9.8This is approximately 4.28 seconds. To prove that this answer is correct, let’s use the following equation.d = vi t + ½ a * t^2, a = -9.8d = 24 (√321.2 + 24) ÷ 9.8 + ½ -9.8 * [(√321.2 + 24) ÷ 9.8]^2This is exactly 13 meters. This proves that the time is correct. There are two answers because the velocity at this height is either +√321.2 m/s or -+√321.2 m/s. I hope this is helpful for you. http://www.mathguide.com/lessons2/FlightProjectile...If you go to the website above, you will see graphs of height versus time for a projectile. The graph is shaped like an inverted parabola. This is reason that the stone can have the same speed and height at two different times.

Hermina Ferry · Answer

Solution:(a) v² = u² + 2 a s=> v² = 24² + 2 x (-9.8) x 13=> v = 17.9 m/s(b)x = u t + 0.5 a t²=> 13 = 24t + 0.5 x (-9.8) x t² => 4.9t² - 24t + 13 = 0 [ t = 0.62 s or 4.28 stime taken to reach the height of 13 m the first time round is 0.62 s.(c)From (b) above, we can see the quadratic equation can generate 2 answers.However, that is not the reason for 2 answers to (b).The reason is the stone has not reached its maximum height when it reaches the height of 13 m.So, the stone reaches the height of 13 m first before it proceeds to its maximum height.Thereafter, at time = 4.28 s, the stone falls back down to the height of 13 m the second time round.Hence, there are two answers to (b).*note: maximum height is 29.4 msee calculation of maximum height: K.E. at the lowest point = P.E. at the highest point=> 0.5 m v² = m g h=> v² = 2 g h=> h = 0.5 (24)² / 9.8 = 29.4 mhope this helps.

Jakob Littel

A stone is thrown vertically upward with a speed of 24 m/s?

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