A stone is thrown vertically upwards with an initial velocity 20m/s. Find the maximum height it reaches and the time taken by it to reach the height. (g= 10m/s)

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The maximum height it reaches is 20 meters

The time taken by it to reach the height is 2 seconds

Step-by-step explanation:

The formula of the height of the stone is h = u t - g t², where

∵ A stone is thrown vertically upwards with an initial velocity of 20 m/s

∴ u = 20 m/s

∵ g = 10 m/s²

→ Substitute them in the equation above

∴ h(t) = 20t - (10) t²

∴ h(t) = 20t - 5t²

→ Arrange the terms of the right side according to the greatest power of t

∴ h(t) = -5t² + 20t

To find the maximum height and the time of it find the vertex of the quadratic function (m, k), where m = and k is the value of h at t = m, a is the coefficient of t² and b is the coefficient of t

∵ The coefficient of t² is -5

∴ a = -5

∵ The coefficient of t is 20

∴ b = 20

→ Use them to find h

∵ m = = = h

∴ m = 2

→ Substitute it in the equation above to find k

∵ h(m) = k

∵ k = -5(2)² + 20(2)

∴ k = -5(4) + 40

∴ k = -20 + 40

∴ k = 20

∴ The coordinate of the vertex of the function are (2, 20)

→ m represents the time of the maximum height and k represents

  the maximum height

∴ The maximum height it reaches is 20 meters

∴ The time taken by it to reach the height is 2 seconds

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