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

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/s².

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.