Long jump: inital center of mass height of 1.08 m, final center of mass height of 0.42 m, projection velocity of 8.7 m/s, projection angle of 22.3 degrees, and leg extension of 77 m.

1) how long does it take to reach maximum jump height? a. 0.337 s b. 0.674 s c. 0.821 s d. 0.887 s

2) what is the maximum center of mass height off of the ground? a. 1.08 m b. 1.64 m c. 4.38 m d. 4.94 m

3) what is the time of flight? a. 0.586 s b. 0.674 s c. 0.834 s d. 0.915 s

4) what is the distance of jump? a. 6.20 m b. 7.49 m c. 8.03 m d. 8.73 m

1) The maximum jump height is reached at A.

2) The maximum center of mass height off of the ground is B.

3) The time of flight is C.

4) The distance of jump is B.

Explanation:

First of all we need to decompose velocity in its rectangular components, so

1) We use, , as we clear it for and using the fact that at max height, we obtain

2) We can use the formula for , so

3) We can use the formula , to find total time of fligth, so , as it is a second-grade polynomial, we find that its positive root is

4) Finally, we use , as it has an additional displacement of due the leg extension we obtain,

, aprox

convex lenses are thicker at the middle. rays of light that pass through the lens are brought closer together (they converge). a convex lens is a converging lens. when parallel rays of light pass through a convex lens the refracted rays converge at one point called the principal focus.

see earlier