In her physics lab, Stephanie rolls a 30 g marble down a ramp and off a table with a horizontal velocity of 2 m/s. The marble falls in a cup placed 0.4 m from the table’s edge.
a. How long is the ball in the air?
0.2 s
b. How high is the table? m
h = 1/2 at^2
You have a & t. Plug and chug
To find the height of the table, we can use the equation of motion for vertical motion. The equation is:
y = y0 + v0y * t - (1/2) * g * t^2
Where:
- y is the vertical displacement (height in this case)
- y0 is the initial vertical position (0 in this case since we are measuring from the ground)
- v0y is the initial vertical velocity (0 in this case since the marble is only given a horizontal velocity)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- t is the time the ball is in the air
We can solve for y by substituting the given values into the equation and solving for y.
Given:
- y0 = 0 (initial vertical position)
- v0y = 0 (initial vertical velocity)
- g = 9.8 m/s^2
- t = 0.2 s (time in the air)
Plugging the values into the equation:
y = 0 + 0 * 0.2 - (1/2) * 9.8 * (0.2)^2
y = 0 - 0 + (1/2) * 9.8 * 0.04
y = 0 + 0.196
y = 0.196 m
Therefore, the height of the table is 0.196 meters.