Predict the horizontal distance a cannon on a 15 m cliff will shoot if it's initial velocity is 140 m/s and it's inclined at 15 degrees.
Just plug in your values and solve for y=0 in the equation of motion:
y = 15 + x tanθ - g/(2(v cosθ)^2) x^2
To predict the horizontal distance a cannon on a 15 m cliff will shoot, with an initial velocity of 140 m/s and inclined at 15 degrees, we can follow these steps:
Step 1: Resolve the initial velocity into horizontal and vertical components:
The horizontal component is given by Vx = V * cos(theta), where V is the initial velocity and theta is the angle of inclination.
Vx = 140 m/s * cos(15 degrees)
Vx ≈ 134.42 m/s
The vertical component is given by Vy = V * sin(theta), where V is the initial velocity and theta is the angle of inclination.
Vy = 140 m/s * sin(15 degrees)
Vy ≈ 36.09 m/s
Step 2: Determine the time it takes for the projectile to reach the ground.
Since the cliff is 15 m high, the vertical displacement is -15 m (negative due to downward direction), and the initial vertical velocity is 36.09 m/s (as calculated above).
Using the kinematic equation: displacement = (initial velocity * time) + (0.5 * acceleration * time^2), with acceleration due to gravity (g) equal to -9.8 m/s^2, we can rearrange the equation to solve for time:
-15 m = (36.09 m/s * t) + (0.5 * -9.8 m/s^2 * t^2)
-15 = 36.09t - 4.9t^2
This equation is a quadratic equation that can be solved using various methods, such as factoring, quadratic formula, or graphical methods.
Solving the equation, we find two possible values for time: t = 0.9434 s (ignoring negative time) and t = 7.0256 s.
Step 3: Calculate the horizontal distance traveled by the projectile.
Using the horizontal component of the initial velocity (Vx = 134.42 m/s) and the time it takes for the projectile to reach the ground (t = 0.9434 s), we can calculate the horizontal distance (d) using the equation: d = Vx * t.
Plugging in the values, we get:
d = 134.42 m/s * 0.9434 s
d ≈ 126.90 m
Therefore, the horizontal distance a cannon on a 15 m cliff will shoot, with an initial velocity of 140 m/s and inclined at 15 degrees, is approximately 126.90 meters.
To predict the horizontal distance a cannon will shoot, we can use the principles of projectile motion. Here's how you can calculate it step-by-step:
Step 1: Break down the initial velocity into its horizontal and vertical components.
Since the cannon is inclined at 15 degrees, we need to resolve the initial velocity into horizontal and vertical components. The horizontal component (Vx) can be calculated as V * cos(θ), and the vertical component (Vy) can be calculated as V * sin(θ), where V is the initial velocity and θ is the angle of inclination.
Vx = 140 m/s * cos(15°)
Vy = 140 m/s * sin(15°)
Step 2: Determine the time of flight.
The time of flight, which is the time it takes for the projectile to reach the ground, can be calculated using the vertical component of velocity. The formula is t = (2 * Vy) / g, where g is the acceleration due to gravity (9.8 m/s²).
t = (2 * Vy) / g
Step 3: Calculate the horizontal distance.
The horizontal distance (range) can be calculated by multiplying the time of flight by the horizontal component of velocity. The formula is range = Vx * t.
range = Vx * t
Now let's substitute the values into the formulas:
Vx = 140 m/s * cos(15°)
Vy = 140 m/s * sin(15°)
t = (2 * Vy) / g
range = Vx * t
After substituting the values and calculating, you will find the horizontal distance the cannonball will travel from the edge of the cliff.