Question

A 50kg track athlete running at 10.0 m/s jumps over a hurdle. If athlete’s horizontal component of the velocity over the hurdle is 8.8 m/s and the air resistance is disregarded, how high was the jump?

Answer 1

As per the given question,

Mass of the athlete (m)=50 kg

Speed of the athlete (v)=10 m/sec

Let the angle of projection $=\theta$

Let the jump was h meter high.

Horizontal component of the velocity $=v \cos\theta=8.8 m/sec$

$\Rightarrow 10 \cos\theta =8.8$

$\Rightarrow \cos \theta =\dfrac{8.8}{10}=0.88$

$\Rightarrow \theta =28.35^\circ$

Vertical component of the velocity$=v\sin\theta=10 \sin 28.35^\circ$

$\Rightarrow h=\dfrac{v^2\sin^2\theta}{2g}$

$\Rightarrow h=\dfrac{10\times 10 \sin^2 28.35^\circ}{9.8}$

$\Rightarrow h=2.3 m$