Question

King Arthur's knights fire a cannon from the top of the castle wall. The cannonball is fired at a speed of 50m/s and an angle of 30 degrees. A cannonball that was accidentally dropped hits the moat below in 1.5s. How far from the castle wall does the fired cannonball hit the ground?

Answer 1

The fired cannonball hits the ground approximately 65.45 meters away from the castle wall.

Step-by-step explanation:

To find the horizontal distance the fired cannonball hits the ground, we need to calculate the time it takes for the cannonball to hit the ground. Since the fired cannonball and the dropped cannonball both hit the ground in the same time of 1.5 seconds, we can use this time in our calculations. To find the horizontal distance, we can use the formula:

1. d = v * t * cos(theta)

Where:

• d is the horizontal distance
• v is the initial velocity of the cannonball (50 m/s)
• t is the time it takes for the cannonball to hit the ground (1.5 s)
• theta is the angle of elevation (30 degrees)

Substituting the values into the formula, we get:

1. d = 50 * 1.5 * cos(30)
2. d = 65.45 m

Therefore, the fired cannonball hits the ground approximately 65.45 meters away from the castle wall.

Answer 2

The fired cannonball hits the ground approximately 55 meters from the castle wall.

Step-by-step explanation:

To determine the horizontal distance from the castle wall to where the fired cannonball hits the ground, we need to calculate the time it takes for the cannonball to reach the ground. We can use the vertical component of the velocity to do this. The initial vertical component of the velocity can be found using the sine of the launch angle, which gives us (50 m/s) × sin(30°) = 25 m/s. The time it takes for the cannonball to reach the ground can be found using the equation h = (1/2)gt^2, where h is the vertical distance and g is the acceleration due to gravity. Plugging in the values, we get -25 m = (-1/2)(9.8 m/s^2)t^2. Solving for t, we find t ≈ 1.27 s. Now, we can use the horizontal component of the velocity to calculate the horizontal distance. The initial horizontal component of the velocity can be found using the cosine of the launch angle, which gives us (50 m/s) × cos(30°) = 43.3 m/s. The horizontal distance can be found using the equation d = v × t, where d is the horizontal distance and v is the horizontal component of the velocity. Plugging in the values, we get d ≈ (43.3 m/s) × (1.27 s) = 55 m. Therefore, the fired cannonball hits the ground approximately 55 meters from the castle wall.