Question

A ball rolls off a desk at a speed of 2 m/s and lands 0.50 seconds later.
a. How far from the base of the desk does the ball land?
b. How high is the desk?

Answer 1

Answer:

(a) The ball lands 1 m ahead of the desk's base.

(b) The height of the desk is 1.225 m.

Explanation:

Given:

Initial velocity of the ball is, $u_{0}=2\ m/s$

Time of flight of the ball is, $t=0.50\ s$

(a)

Let the ball fall at a distance of $x$ from the base of the desk and let the height of the desk be $y$.

The given motion of the ball is a projectile motion that can be divided into 2 mutually perpendicular directions.

Now, considering only the horizontal motion of the ball. The ball not under the influence of any force in the horizontal direction.

Therefore, the distance covered by the ball horizontally is given as:

$x=v_0\times t\\x=2\times 0.50=1\ m$

So, the ball lands 1 m ahead of the desk's base.

(b)

Now, consider only the vertical motion of the ball. The ball is under the influence of gravity.

So, vertical distance can be obtained  using Newton's equations of motion.

We use the following equation of motion:

$y-y_0=u_{oy}t+\frac{1}{2}gt^2$

Where,

$y_{0}\rightarrow \textrm{initial vertical position of ball}\\u_{oy}\rightarrow \textrm{initial vertical velocity}\\g\rightarrow \textrm{acceleration due to gravity}\\y\rightarrow \textrm{final position of ball vertically}$

Here, as the ball leaves the desk horizontally, initial velocity is only in the horizontal direction and doesn't have any component in the vertical direction. So, $u_{oy}=0\ m/s$

Plug in $y_0=h,y=0,g=-9.8,u_{oy}=0,t=0.5$. Solve for $h$.

$0-h=0+\frac{1}{2}(-9.8)(0.5)^2\\-h=-4.9\times 0.25\\h=1.225\ m$

Therefore, the height of the desk is 1.225 m.