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
50 meters plus whatever, find whatever
v = Vi - 0.981 t
v = 0 at max height
so
t = 30 m/s / 9.81 m/s^2
t = 3.06 seconds upward
h = 50 + Vi t - 4.9 t^2
h = 50 + 30 (3.06) - 4.9 (3.06)^2
KE=1/2mv^2
KE=1/2 x m x 900
KE= 450m
GPE at top = KE at bottom
mgh=450m
g=9.81
h=450m/9.81m
h=45.87
45.87m+50m=95.87m
To determine the maximum height reached by the stone, you can use the equations of motion. Assuming the upward direction is positive, and neglecting air resistance, the initial velocity (u) is 30 m/s, the acceleration (a) due to gravity is -9.8 m/s^2 (negative as it acts in the opposite direction), and the displacement (s) is the maximum height reached (h).
The equation to calculate the final velocity (v) when the stone reaches its maximum height is:
v^2 = u^2 + 2as
Substituting the given values, we can solve for v:
v^2 = (30)^2 + 2*(-9.8)*s
v^2 = 900 - 19.6s
When the stone reaches its maximum height, the final velocity is zero (v = 0). So we can rewrite the equation as:
0 = 900 - 19.6s
Simplifying the equation:
19.6s = 900
s = 900 / 19.6
s ≈ 45.92 m
Therefore, the stone reaches a maximum height of approximately 45.92 meters from the ground.
To determine the maximum height reached by the stone, we need to use the equations of motion. Here's how you can calculate it:
1. Identify the given values:
- Initial velocity (u) = 30 m/s (upward)
- Height of the tower (h) = 50 m
2. Understand the concept:
- When the stone is projected vertically upwards, its final velocity (v) becomes zero at the maximum height.
- The time taken (t) to reach the maximum height can be calculated using the equation: v = u - gt, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
- Using the value of t, we can determine the maximum height attained by the stone using the equation: h = ut - 0.5gt^2.
3. Calculate the time taken to reach the maximum height:
v = u - gt
0 = 30 - 9.8t
t = 30 / 9.8
t ≈ 3.06 seconds
4. Calculate the maximum height attained:
h = ut - 0.5gt^2
h = (30 * 3.06) - 0.5 * 9.8 * (3.06)^2
h ≈ 45.68 meters
Therefore, the maximum height reached by the stone from the ground is approximately 45.68 meters.