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Expert-verified Found in: Page 67 ### Physics Principles with Applications

Book edition 7th
Author(s) Douglas C. Giancoli
Pages 978 pages
ISBN 978-0321625922 # How could you determine the speed a slingshot imparts to a rock, using only a meter stick, a rock, and the slingshot?

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.

See the 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.

$u=R·\sqrt{\frac{g}{2}}$ ### Want to see more solutions like these? 