Chapter 3, Problem 10Q

How could you determine the speed a slingshot imparts to a rock, using only a meter stick, a rock, and the slingshot?

Solution

The ways to determine the speed that a slingshot imparts to a rock, using only a meter stick, a rock, and the slingshot.

Solution:

By using the concept of projectile motion.

Explanation:

  

Let the height of building beh (measured by meter stick).

Measure the range of stone dbymeter stick.

Find the time during which stone remains in the air.

Initial velocity in vertical direction, $u_y=0$

Acceleration in vertical direction, ${\text{a}}_y=g$

Displacement in vertical direction (using second equation of motion), $h=u_{y}t+\frac{1}{2}{a}_y{t}^2$

Substitute all the values:

  $\begin{array}{l}h=u_{y}t+\frac{1}{2}{a}_y{t}^2\\ h=0+\frac{1}{2}g{T}^2\end{array}$

  $T=\sqrt{\frac{2h}{g}}$

Motion in horizontal direction: uniform motion i.e.acceleration in horizontal direction is zero.

So, initial speed in the horizontal direction can be found by:

  $\begin{array}{l}v=\frac{d}{T}\\ v=\frac{d}{\sqrt{\frac{2h}{g}}}=d\sqrt{\frac{g}{2h}}\end{array}$

Hence, by measuring d and hwe can find out the speed of the stone.

Conclusion:

By using the concept of projectile motion from a building, we can determine the speed a slingshot imparts to a rock, using only a meter stick, a rock,and the slingshot.