Please give clear explanation of the following problem: A high jumper attempts t

Question

Please give clear explanation of the following problem:

A high jumper attempts to clear a bar that is 1.2 m higher than their centre of mass. The jumper runs towards the high jump and takes off at an angle of 55 from the horizontal. The horizontal component of their velocity at take-off is 3.8 m/s. In your calculations below, treat the person as a point object.

(a) To jump upwards, the high-jumper pushes hard down on the ground. Explain why this causes the person to rise upwards.

(b) What must be the vertical component of the take-off velocity if the person is just able to clear the bar?

(c) At what distance from the high jump must the person take-off so that they just clear the bar?

Explanation / Answer

height of the bar h=1.2 m

angle, thete=55 degrees

ux=3.8 m/sec

a)

to rise the upward, high jumper pushes hard down the ground,

because, person pushes the ground hardly then ground also applies the force upward with same magnitude,

hence, jumper will move upward direction

b)

let,

initial velocity is u

maximum height H=u^2*sin^2(theta)/2g

1.2=u^2*sin^2(55)/(2*9.8)

u=5.92 m/sec

and

vertical velocity uy=u*sin(theta)

uy=5.92*sin(55)

uy=4.85 m/sec

c)

horizontal distance, d=u^2*sin(2*theta)/2*g

d=5.92^2*sin(2*55)/(2*9.8)

d=1.68 m

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