A cannon is fired from the ground at an angle of 30 degrees. It is being shot an an initial velocity of 200m/s. What is the maximum height of the cannon ball? How fat will the cannon ball travel before it hits the ground
the vertical speed is 200 sin30 = 100 m/s
So, the height is
h(t) = 100t - 4.9t^2
As you recall from algebra I, the vertex of the parabola is at t = -b/2a, which in this case is 100/9.8
So, plug that in to get the max height.
The ball is in the air twice that long, and you know the horizontal speed is 200 cos30, so just multiply speed*time to get distance.
what is the answer to my question?
A canon was fired with a muzzle velocity of 100 m/s, mounted at an angle of 30 degrees above the ground.
To find the maximum height of the cannonball, we need to calculate the vertical component of its initial velocity.
Using trigonometry, we can determine that the vertical component is given by:
Vertical Component = Initial Velocity * sin(angle)
Plugging in the values, we have:
Vertical Component = 200 m/s * sin(30°)
Now, let's calculate the maximum height. At the maximum height, the vertical velocity becomes zero (as the cannonball momentarily stops moving upwards before falling back). We can use the equation:
Final Velocity^2 = Initial Velocity^2 + 2 * acceleration * distance
Since the final vertical velocity is zero, we can modify the equation to find the displacement (maximum height):
0 = (Vertical Component)^2 - 2 * g * (maximum height)
Rearranging the equation, we get:
maximum height = (Vertical Component)^2 / (2 * g)
Now, let's plug in the values:
maximum height = (200 m/s * sin(30°))^2 / (2 * 9.8 m/s^2)
Calculate the expression above, and you will find the maximum height of the cannonball.
To find how far the cannonball will travel before hitting the ground, we need to calculate the horizontal component of its initial velocity.
Using trigonometry, we can determine that the horizontal component is given by:
Horizontal Component = Initial Velocity * cos(angle)
Plugging in the values, we have:
Horizontal Component = 200 m/s * cos(30°)
Now, we can calculate the time it takes for the cannonball to hit the ground using the vertical component:
Time = 2 * Vertical Component / g
Finally, we can find how far the cannonball will travel by multiplying the horizontal component by the time:
Distance = Horizontal Component * Time
Plug in the values and calculate the expression above, and you will find the distance traveled by the cannonball before hitting the ground.