Question

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

Short answer

Using the slingshot, you can launch rock in a horizontal projection from a height of 1 m. Then use the following formula to calculate initial velocity u.

$u=R·\sqrt{\frac{g}{2}}$

Here, R is the horizontal range measured by a meter stick, and g is acceleration due to gravity.

Step-by-step solution

Step 1. Understanding horizontal projection

When a projectile is launched such that its initial velocity is in the horizontal direction and the vertical component of initial velocity is zero, it is called horizontal projection.

Step 2. Range of a horizontal projection

Consider a horizontal projection launched from an initial height H above the ground, with initial velocity u. As velocity in the vertical direction is zero, the time taken by the projectile to hit the ground can be written using the second equation of motion.

$-H=0+\frac{1}{2}\left(-g\right)t^2$

Solving the above equation for t,

$t=\sqrt{\frac{2H}{g}}$.

As there is no external force in the horizontal direction (neglecting air resistance), the horizontal distance (R) covered in this time can be written as

$R=u·\sqrt{\frac{2H}{g}}$.

This is the formula for the range of a horizontal projectile fired from a height H.

Step 3. Calculating the initial speed of the slingshot

A rock is launched in a horizontal projection from a height of 1 m using a slingshot. You can measure the horizontal range using the meter scale.

Substitute the values in the above formula to calculate the initial speed.

$u=R·\sqrt{\frac{g}{2}}$