In the vertical jump, an athlete starts from a crouch and jumps upward as high as possible. Even the best athletes spend little more than 1.00 s in the air (their ""hang time""). Treat the athlete as a particle and let [math]y_{\max }[/math] be his maximum height above the floor. To explain why he seems to hang in the air, calculate the ratio of the time he is above [math]y_{\max } / 2[/math] to the time it takes him to go from the floor to that height.

6.82842712475

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

g = Acceleration due to gravity = 9.81 m/s²

m denotes max

b denotes below

a denotes above

Substituting u in the above equation

Now

Solving the equation

The ratio is

The ratio is 6.82842712475

the chart show the masses and velocities of two colliding objects that stick together after a collision.

according to the law of conservation of momentum, the momentum of the object after the collision is  

answer

1,500

kg • m/s.