A stone projected vertically upward with a speed of 30ms from the top of a tower of height 50m neglecting the air resistance.determine the maximum height it reach from the ground

recall that the height

h(t) = 50 + 30t - 4.9t^2
And as with all parabolas ax^2+bx+c, the vertex is at x = -b/2a

ho = 50 m = ht. of tower.

h1 = ht above the tower.
h = ht. above gnd.

V^2 = Vo^2 + 2g*h1 = 0,
30^2 + (-19.6)*h1 = 0,
h1 = 45.9 m.

h = ho + h1 = 50 + 45.9 = __ m. above gnd.

To determine the maximum height reached by the stone, we need to analyze the motion of the stone in two phases: the upward journey and the downward journey.

1. Upward Journey:
During the upward journey, the initial velocity of the stone is 30 m/s, and it is moving against gravity. The acceleration due to gravity is 9.8 m/s² (assuming Earth's gravity is constant).
Using the kinematic equation:
v² = u² + 2as, where
v = final velocity (0 m/s at the maximum height),
u = initial velocity (30 m/s),
a = acceleration (-9.8 m/s²),
s = displacement (unknown - maximum height).

Substituting the values into the equation, we have:
0² = 30² + 2(-9.8)s
0 = 900 - 19.6s
19.6s = 900
s = 900 / 19.6 ≈ 45.92 m

Therefore, during the upward journey, the stone reaches a maximum height of approximately 45.92 meters.

2. Downward Journey:
During the downward journey, the stone is in free fall, so it covers the same distance as during the upward journey.
Therefore, the maximum height reached by the stone from the ground is also approximately 45.92 meters.

Hence, neglecting air resistance, the stone reaches a maximum height of approximately 45.92 meters from the ground.