Questions: In her Physics Lab, Melanie rolls a 10 g marble down a ramp and off the table with a horizontal velocity of 0.5 m / s / s. The marble falls in a cup placed 0.51 m from the table's edge. How high is the table?

In her Physics Lab, Melanie rolls a 10 g marble down a ramp and off the table with a horizontal velocity of 0.5 m / s / s. The marble falls in a cup placed 0.51 m from the table's edge. How high is the table?

Transcript text: 3. [cp p30 6] In her Physics Lab, Melanie rolls a 10 g marble down a ramp and off the table with a horizontal velocity of $0.5 \mathrm{~m} / \mathrm{s} / \mathrm{s}$. The marble falls in a cup placed 0.51 m from the table's edge. How high is the table?[0.92 m]

Solution

Solution Steps

Step 1: Determine Time of Flight

Use the horizontal motion to find the time of flight.
The horizontal distance $d$ is 0.51 m, and the horizontal velocity $v_x$ is $0.5 \, \mathrm{m/s}$.
Use the formula: $ t = \frac{d}{v_x} $.

Step 2: Calculate Time

Substitute the known values: $ t = \frac{0.51 \, \mathrm{m}}{0.5 \, \mathrm{m/s}} $.
Calculate $ t $.

Step 3: Determine Height of the Table

Use the vertical motion to find the height of the table.
The initial vertical velocity is 0, and the acceleration due to gravity $g$ is $9.8 \, \mathrm{m/s^2}$.
Use the formula: $ h = \frac{1}{2} g t^2 $.

Step 4: Calculate Height