Question

A physics lab group rolls a ball off a horizontal table with a speed of 1.6 m/s. the table is 1.2 m high. how far in the horizontal direction does the ball travel before it hits the floor?

Answer 1

0.784 m

Step-by-step explanation:

The motion of the ball is a projectile motion, which consists of two independent motions:

- a horizontal uniform motion, with constant speed of
`v_0 = 1.6 m/s`

- a vertical accelerated motion, with constant acceleration
`g=-9.8 m/s^2` towards the ground and initial position
`y_0 = 1.2 m`

By looking at the vertical motion, we can find the time t at which the ball hits the ground, which is the time t at which the vertical position y becomes zero:

`y(t)=0\\y(t)=y_0 +(1)/(2)gt^2\\0=y_0 +(1)/(2)gt^2\\t=\sqrt{-(2 y_0)/(g)}=\sqrt{-(2\cdot 1.2 m)/(-9.8 m/s^2)}=0.49 s`

And now we can use the horizontal motion to find the total horizontal distance traveled during this time interval:

`S_x = v t=(1.6 m/s)(0.49 s)=0.784 m`