A stone is projected upward at an angle of 30 degree to the horizontal from the top of a tower 100m and it hits the ground at a point q. If the initial veloity of projection is 100ms cal the maximum height of the stone above the groud
The vertical component of the velocity is needed. Therefore
from v=u + gt
0=usintita +gt
100sin30 = 10t
t=5s.
so it takes 5 sec to get to the max height when thrown from the top of the building. To find the additional distance(height) travel we use this:
S= ut + 1/2gt2.
S= 0 + 1/2*10*25
S= 125m.
Therefore total height is 100+125=225m.
I hope that piece above was helpful
How do you solve it
Vo = 100m/s[30o].
Yo = 100*sin30 = 50 m/s.
Y^2 = Yo^2 + 2g*h.
h = (Y^2-Yo^2)/2g + ho.
y = 0.
g = -9.8 m/s^2.
ho = 100 m.
h = ?
23
Well, if the stone hits the ground, it sounds like its dreams of becoming an astronaut have come crashing down! Anyway, let's calculate the maximum height.
To find the maximum height, we need to first determine the time it takes for the stone to reach the highest point of its trajectory. We know the initial velocity of the stone is 100 m/s and it moves vertically, so we can use the formula:
t = (Vf - Vi)/(-g)
where:
- Vf is the final vertical velocity (which will be 0 m/s at the highest point),
- Vi is the initial vertical velocity (which, in this case, is 100 m/s),
- g is the acceleration due to gravity (which is approximately 9.8 m/s²).
Plugging in the values, we get:
t = (0 - 100)/(-9.8)
t = 10.2 seconds (approximately)
Now that we have the time taken to reach the highest point, we can calculate the maximum height using the formula:
h = Vi * t + (1/2) * (-g) * t²
Substituting in the values:
h = 100 * 10.2 + (1/2) * (-9.8) * (10.2)²
h ≈ 1020 - 500
h ≈ 520 meters
Therefore, the maximum height of the stone above the ground is approximately 520 meters. I hope that brought a little height to your day!
To find the maximum height of the stone above the ground, we can break down the motion of the stone into horizontal and vertical components.
The initial velocity of projection can be broken down into its horizontal and vertical components using the angle of projection. The horizontal component (Vx) can be found using cosine function:
Vx = initial velocity * cos(angle)
Vx = 100 m/s * cos(30°)
Vx = 100 m/s * √3/2
Vx ≈ 86.60 m/s
The vertical component (Vy) can be found using sine function:
Vy = initial velocity * sin(angle)
Vy = 100 m/s * sin(30°)
Vy = 100 m/s * 1/2
Vy = 50 m/s
Now, let's focus on the vertical motion of the stone. We can use the kinematic equation to find the maximum height (h_max) reached by the stone:
Vy^2 = Vy0^2 - 2g * h_max
Since the stone is projected upwards, the initial vertical velocity (Vy0) is positive (50 m/s), and acceleration due to gravity (g) is negative (-9.8 m/s^2).
Plugging in the values, we have:
(50 m/s)^2 = (50 m/s)^2 - 2 * -9.8 m/s^2 * h_max
Simplifying, we get:
2500 m^2/s^2 = 2500 m^2/s^2 + 19.6 m/s^2 * h_max
Now, let's solve for h_max:
2500 m^2/s^2 - 2500 m^2/s^2 = 19.6 m/s^2 * h_max
0 m^2/s^2 = 19.6 m/s^2 * h_max
Therefore, h_max = 0.
Since the equation gives us h_max = 0, it means that the stone does not reach any maximum height above the ground. It directly falls from the top of the tower to the ground without reaching its maximum height.