Question

pls help A ball rolls horizontally off a 100-meter-tall cliff at 40 meters per second. How far does the ball travel horizontally before reaching the ground? (Neglect air resistance.)
A. 100 meters
B. 200 meters
C. 300 meters
D. 400 meters

Answer 1

First find the time it takes for the ball to reach the ground using the vertical component of its position vector:

$y=y_0+v_{0y}t+\dfrac12a_yt^2$

$\implies0=100\,\mathrm m+\dfrac12\left(-9.8\,\dfrac{\mathrm m}{\mathrm s^2}\right)t^2$

$\implies t=4.52\,\mathrm s$

Meanwhile, the horizontal component of the ball's position vector is

$x=x_0+v_{0x}t+\dfrac12a_xt^2$

$\implies x=\left(40\,\dfrac{\mathrm m}{\mathrm s}\right)t$

After about 4.52 s, the ball has traveled a horizontal distance of

$x=\left(40\,\dfrac{\mathrm m}{\mathrm s}\right)(4.52\,\mathrm s)=180.8\,\mathrm m$

which you would round to 200 m, so the answer is B.