A baseball is hit off the edge of a cliff horizontally at a speed of 30 m/s. It takes the ball 3 seconds to reach the ground, with no air resistance. How high is the cliff wall?
This is a free fall situation.
The horizontal velocity has no effect on the time to reach ground.
Vertical distance,
X=0+(1/2)at^2
=0+(1/2)(-9.81)*3^2
=44 m approximately.
To determine the height of the cliff wall, we can use the equation of motion for the vertical motion of the baseball. The equation is:
h = v₀t + (1/2)gt²
Where:
h is the vertical displacement or height
v₀ is the initial vertical velocity, which is zero because the ball was hit horizontally
t is the time taken to reach the ground, which is 3 seconds
g is the acceleration due to gravity, which is approximately 9.8 m/s²
Using these values, we can plug them into the equation to find the height:
h = (0)(3) + (1/2)(9.8)(3²)
h = 0 + (1/2)(9.8)(9)
h = (1/2)(9.8)(9)
h = (4.9)(9)
h = 44.1 meters
Therefore, the height of the cliff wall is approximately 44.1 meters.
To determine the height of the cliff wall, we can use the kinematic equation for vertical motion:
h = (1/2) * g * t^2
In this equation, "h" represents height, "g" represents the acceleration due to gravity (approximately 9.8 m/s^2 on Earth), and "t" represents the time of flight (3 seconds in this case).
First, we need to calculate the horizontal distance the ball traveled during the 3-second time of flight.
d = v * t
Given that the initial horizontal velocity (v) is 30 m/s and the time of flight (t) is 3 seconds, we can determine the horizontal distance (d).
d = 30 m/s * 3 s = 90 meters
Now, we have the horizontal distance (d) the ball traveled during the 3 seconds it took to reach the ground. Since there was no horizontal acceleration, we can say that the horizontal distance (d) is equivalent to the horizontal displacement of the ball.
To find the height of the cliff wall (h), we need to calculate the vertical distance traveled by the ball.
Using the equation:
h = (1/2) * g * t^2
where g is the acceleration due to gravity (9.8 m/s^2) and t is the time of flight (3 seconds), we can substitute the values and solve for h.
h = (1/2) * 9.8 m/s^2 * (3 s)^2
h = 1/2 * 9.8 m/s^2 * 9 s^2
h = 1/2 * 9.8 m/s^2 * 81
h = 1/2 * 9.8 * 81 m
h = 396.9 meters
Therefore, the height of the cliff wall is approximately 396.9 meters.