An arrow is shot horizontally from a cliff at 15 m/s land 30 m away. How high is the cliff?
the arrow travels for 2 seconds
in 2 seconds, it falls 4.9*2^2 = 19.6m
Well, let's do some calculations, shall we? So, according to my highly advanced calculations, the time it takes for the arrow to land 30 meters away horizontally is given by the equation t = d/v, where d is the distance and v is the velocity. Now, since the velocity is given as 15 m/s and the distance is 30 meters, we can find the time as t = 30/15 = 2 seconds.
Here comes the fun part! Since the arrow was shot horizontally, we can use the equation h = 0.5gt^2 to find the height of the cliff. But what's g, you ask? Well, g is the acceleration due to gravity, which is approximately 9.8 m/s^2.
Now, plugging in the value of time (t = 2 seconds) into the equation, we get h = 0.5 * 9.8 * (2^2). Solving this mathematical masterpiece, we find that the height of the cliff is approximately 19.6 meters.
So, there you have it! The height of the cliff is about 19.6 meters. Just remember to duck when throwing any boomerangs near cliffs, you know, just in case!
To find the height of the cliff, we can use the equation of motion for horizontal motion.
The horizontal motion of the arrow is unaffected by gravity, so we can use the equation: distance = velocity × time.
Given that the distance is 30 m and the horizontal velocity is 15 m/s, we can rearrange the equation to solve for time: time = distance / velocity.
Substituting the given values, we have: time = 30 m / 15 m/s.
Calculating this, we get: time = 2 seconds.
Since the arrow is shot horizontally, it takes 2 seconds to reach the 30-meter distance.
Next, we can use the vertical motion equation to find the height of the cliff.
The equation for vertical motion is: height = initial velocity × time + 0.5 × acceleration × time^2.
The initial vertical velocity is 0 m/s because the arrow is shot horizontally.
The acceleration due to gravity is approximately 9.8 m/s^2 (assuming no air resistance).
Plugging in these values, we have: height = 0 × 2 + 0.5 × 9.8 × 2^2.
Simplifying this equation, we get: height = 0 + 0.5 × 9.8 × 4.
Calculating this, we find: height = 19.6 meters.
Therefore, the height of the cliff is approximately 19.6 meters.
To find the height of the cliff, we can use the equations of motion to analyze the vertical motion of the arrow.
First, let's list the known values:
- Initial velocity in the horizontal direction (vx) = 15 m/s
- Horizontal distance covered (x) = 30 m
- Acceleration in the vertical direction (ay) = -9.8 m/s² (assuming downward motion due to gravity)
We need to find the height of the cliff (h).
Since the arrow is shot horizontally, there is no initial vertical velocity (vy).
We can use the equation for vertical displacement (Δy) as a function of time:
Δy = vy*t + (1/2)*ay*t²
Since the arrow takes the same amount of time to reach the ground horizontally (30 m) as it does vertically (h), we can set the equations for both horizontal and vertical motion equal to each other:
x = vx*t
Δy = vy*t + (1/2)*ay*t²
Now, we can eliminate the time (t) from both equations by using the fact that t = x/vx:
Δy = vy*(x/vx) + (1/2)*ay*(x/vx)²
Substituting the known values:
Δy = 0 + (1/2)*(-9.8)*((30/15)²)
Simplifying the equation:
Δy = -4.9*(2²)
Δy = -4.9*4
Δy = -19.6 m
The negative sign indicates that the displacement is in the downward direction. Therefore, the height of the cliff is 19.6 meters.