Question

In the high jump, the kinetic energy of an athlete is transformed into gravitational potential energy without the aid of a pole. Find the minimum speed must the athlete leave the ground in order to lift his center of mass 1.95 m and cross the bar with a speed of 0.95 m/s

Answer 1

6.25 m/s

Step-by-step explanation:

When the athlete is running toward the high bar, all his energy is KE. As he crosses over the top of the bar, he has both KE and PE.

KE = 1/2mv²

PE = mgh

v₁ = initial velocity (launch velocity)

v₂ = velocity at top of bar

1/2mv₁² = mgh + 1/2mv₂²

mass drops out

1/2v₁² = (9.8 m/s²)(1.95 m) +1/2(0.95 m/s)²

1/2v₁² = (19.11 m²/s²) + (0.45 m²/s²)

v₁² = 2(19.56 m²/s²)

v₁ = √39.12 m²/s² = 6.25 m/s