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

Answer:

0.784 m

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:

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

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

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