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Q11.

Expert-verifiedFound in: Page 67

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*.

$u=R\xb7\sqrt{\frac{g}{2}}$

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

**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.**

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

$R=u\xb7\sqrt{\frac{2H}{g}}$.

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

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.

$u=R\xb7\sqrt{\frac{g}{2}}$

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