a ball rolls horizontally with a speed of 7.6 m/s off the edge of a tall platform. if the ball lands 8.7 m from the point on the ground directly below the edge of the platform, what is the height of the platform?
the horizontal speed never changes, so you can figure out how long it is in the air by distance = rate times time
then figure out how far it fell in that amount of time starting with zero vertical velocity.
Why did the ball roll off the platform?
Because it wanted to prove that gravity can be a real downer!
In all seriousness, let's solve this problem. We can use the equation of motion for vertical motion to find the height of the platform.
First, let's find the time it takes for the ball to fall to the ground. Using the equation s = ut + (1/2)gt^2, where s is the distance, u is the initial vertical velocity (which is zero in this case), g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
Plugging in the values:
8.7 = (1/2) × 9.8 × t^2
Now let's solve for t:
16.1 = 9.8 × t^2
t^2 = 16.1 / 9.8
t ≈ √(16.1 / 9.8)
t ≈ √1.642
t ≈ 1.28 seconds
Now that we know the time, we can find the height of the platform using the equation:
h = ut + (1/2)gt^2
h = 0 × 1.28 + (1/2) × 9.8 × 1.28^2
h ≈ (1/2) × 9.8 × 1.64
h ≈ 8.0 meters
So, the height of the platform is approximately 8.0 meters.
To find the height of the platform, we can use the kinematic equation that relates horizontal distance, initial velocity, and time. The equation is given as:
d = v * t,
where:
d is the horizontal distance traveled,
v is the initial horizontal velocity, and
t is the time taken.
In this scenario, the horizontal distance traveled by the ball is 8.7 m, and the initial horizontal velocity is 7.6 m/s. Therefore, we can rearrange the equation to solve for time:
t = d / v.
Substituting the given values, we get:
t = 8.7 m / 7.6 m/s = 1.1447 s.
Now that we know the time taken, we can use the kinematic equation for vertical motion to find the height of the platform. The equation is given as:
h = v * t + (1/2) * g * t^2,
where:
h is the height of the platform,
v is the initial vertical velocity (which is 0 since the ball is rolling horizontally),
t is the time taken, and
g is the acceleration due to gravity (which is approximately 9.8 m/s^2).
Using the equation, we can calculate the height of the platform:
h = (0 m/s) * 1.1447 s + (1/2) * (9.8 m/s^2) * (1.1447 s)^2 = 6.5363 m.
Therefore, the height of the platform is approximately 6.5363 meters.
To find the height of the platform, we need to use the kinematic equation for horizontal motion.
The equation is:
d = v*t
where:
d is the horizontal distance traveled by the ball (8.7 m),
v is the horizontal velocity of the ball (7.6 m/s), and
t is the time of flight of the ball.
Since the ball rolls horizontally, the vertical motion does not affect the horizontal distance covered. Therefore, we can ignore the vertical motion for this problem.
Now, let's rearrange the equation to solve for time:
t = d / v
Substituting the given values, we have:
t = 8.7 m / 7.6 m/s
t ≈ 1.145 seconds
Next, we can calculate the height of the platform using the kinematic equation for vertical motion. The equation is:
h = (1/2) * g * t^2
where:
h is the height of the platform,
g is the acceleration due to gravity (9.8 m/s^2),
t is the time of flight of the ball.
Plugging in the values:
h = (1/2) * 9.8 m/s^2 * (1.145 s)^2
h ≈ 6.22 meters
Therefore, the height of the platform is approximately 6.22 meters.