Question

A cannonball at ground level is aimed 26 degrees above the horizontal and is fired with an initial speed of 105 m/s. How far from the cannon will the cannonball hit the ground? Give your answer in whole numbers.

Answer 1

To find the distance that the cannonball will hit the ground, we need to use the principles of projectile motion. By using the given information and solving the vertical and horizontal motion equations, we find that the cannonball will hit the ground approximately 642 meters away from the cannon.

Step-by-step explanation:

To solve this problem, we can use the principles of projectile motion. The horizontal and vertical components of motion are independent of each other. Let's break down the information given:

• Initial speed (v0) = 105 m/s
• Launch angle (θ) = 26° above the horizontal
• Vertical acceleration (ay) = -9.8 m/s2 (due to gravity)

First, we can calculate the time it takes for the cannonball to hit the ground. We can use the vertical motion equation: y = v0yt + (1/2)at2. Since the cannonball hits the ground, its final vertical position (y) is 0. We can rearrange the equation to solve for time (t).

Next, we can use the horizontal motion equation: x = v0xt to calculate the horizontal distance (x) traveled by the cannonball.

Using these equations, we can find that the cannonball will hit the ground approximately 642 meters away from the cannon.

Answer 2

The cannonball will hit the ground approximately 1111 meters away from the cannon.

Step-by-step explanation:

To calculate the horizontal distance the cannonball will travel, we can use the horizontal component of its initial velocity. The horizontal component can be found using the formula:

Horizontal component of velocity = initial velocity * cos(angle)

Using the given initial velocity of 105 m/s and the angle of 26 degrees, we can calculate:

Horizontal component of velocity = 105 m/s * cos(26) = 94.24 m/s

To find the time of flight, we can use the equation:

Time of flight = (2 * initial velocity * sin(angle)) / g

Where g is the acceleration due to gravity (approximately 9.8 m/s²). Plugging in the values:

Time of flight = (2 * 105 m/s * sin(26)) / 9.8 m/s² = 11.78 s

The horizontal distance the cannonball will travel is given by:

Distance = horizontal component of velocity * time of flight

Distance = 94.24 m/s * 11.78 s ≈ 1111 m