To take the longest possible jump, an athlete should make an angle of _____

This question was previously asked in

BPSC Asstt. Prof. ME Held on Nov 2015 (Advt. 22/2014)

Option 3 : 45 degree with the ground

CT 10: Soil Mechanics

4421

10 Questions
10 Marks
10 Mins

**Concept:**

Projectile motion:

When a particle is projected obliquely near the earth's surface, it moves simultaneously in horizontal and vertical directions. The **path** of such a particle is called **projectile** and the motion is called **projectile motion**.

**Range of projectile:**

- The horizontal range of a projectile is the
**distance along the horizontal plane**it would travel, before reaching the same vertical position as it started from.

**Formulae in projectile motion:**

\(Range\;of\;projectile = \frac{{{u^2}\sin 2θ }}{g}\)

\(Total\;time\;of\;flight = \frac{{2u\;sinθ }}{g}\)

\(Maximum\;Height = \frac{{{u^2}{{\sin }^2}θ }}{{2g}}\)

where u = projected speed, θ = angle at which an object is thrown from the ground and g = acceleration due to gravity = 9.8 m/s^{2}.

**Calculation:**

**Given:**

Range of a Projectile motion is given by (R):

\(R= \frac{{{u^2}\sin 2θ }}{g}\)

For horizontal distance to be maximum:

sin 2θ = 1

∴ sin 2θ = sin 90°

∴ θ = 45°.

**∴ to take the longest possible jump, an athlete should make an angle of 45° with the ground.**