A projectile is fired with an initial velocity of 193.2 fps upward at an angle 30∘ to the horizontal from point 257.6 ft above the level plain. What horizontal distance will it cover before it strikes the level plain?
you can go at it by finding the flight time:
257.7 + 193.2/2 t - 4.9t^2 = 0
and then the distance is 193.2 * √3/2 * t
A projectile is fired with an initial velocity of 193.2 fps upward at an angle 30° to the
horizontal from a point 257.6 feet above a level plain. What horizontal distance will it cover before it
strikes the level plain?
To find the horizontal distance covered by the projectile before it strikes the level plane, we can use the equations for projectile motion:
1. Split the initial velocity into its horizontal (Vx) and vertical (Vy) components.
Vx = V * cos(θ)
Vy = V * sin(θ)
Given:
Initial velocity (V) = 193.2 fps
Angle (θ) = 30 degrees
Vx = 193.2 * cos(30)
Vx = 193.2 * 0.866025404
Vx ≈ 167.4202492 fps
2. Determine the time taken (t) for the projectile to reach the ground.
Use the equation:
t = (2 * Vy) / g
where g is the acceleration due to gravity (32.174 ft/s²).
Vy = 193.2 * sin(30)
Vy = 193.2 * 0.5
Vy = 96.6 fps
t = (2 * 96.6) / 32.174
t ≈ 6 seconds
3. Calculate the horizontal distance (d) by multiplying the horizontal velocity (Vx) by the time taken (t).
d = Vx * t
d = 167.4202492 * 6
d ≈ 1004.52 ft
Therefore, the projectile will cover approximately 1004.52 feet horizontally before it strikes the level plain.
To find the horizontal distance covered by the projectile before it strikes the level plain, we can use the equations of projectile motion. We'll assume that there is no air resistance.
1. First, let's break down the initial velocity into its horizontal and vertical components.
The horizontal component of the initial velocity (Vx) can be found using the equation:
Vx = initial velocity * cos(angle)
Given:
Initial velocity (Vi) = 193.2 ft/s
Angle (θ) = 30 degrees
Using the cosine function calculator, we find:
Vx = 193.2 ft/s * cos(30°) = 193.2 ft/s * 0.866 = 167.64 ft/s
2. Next, let's find the vertical component of the initial velocity (Vy).
The vertical component of the initial velocity (Vy) can be found using the equation:
Vy = initial velocity * sin(angle)
Using the sine function calculator, we find:
Vy = 193.2 ft/s * sin(30°) = 193.2 ft/s * 0.5 = 96.6 ft/s
3. Now, let's find the time it takes for the projectile to reach the level plain.
The time (t) can be found using the equation:
t = time of flight = 2 * Vy / g
where g is the acceleration due to gravity (32.2 ft/s^2).
t = 2 * 96.6 ft/s / 32.2 ft/s^2 = 6s
4. Finally, let's find the horizontal distance (D) covered by the projectile.
The horizontal distance (D) can be found using the equation:
D = Vx * t
D = 167.64 ft/s * 6s = 1005.84 ft
Therefore, the horizontal distance covered by the projectile before it strikes the level plain is approximately 1005.84 ft.