Jake jumps with an initial velocity of 8ft/sec, and Jake weighs 150 pounds, Calculate...

Question

Jake jumps with an initial velocity of 8ft/sec, Jake weighs 150 pounds.

 

1. What is his hang time on the moon and on the earth. Keep in mind the moon has 1/6 the gravitational pull of the earth?

 

2. What is his maximum jump height in each location?

Answer 1

Mertaug,

 

In order to answer these questions, we need to know a couple of physics formulas for equation of motion.

 

 eqn (1)   v_f - v_i = at

     where v_f is the final velocity

               v_i is the initial velocity

               a is the acceleration due to gravity

               t is time

 

 eqn (2)  v_{f^{2 -}} v_i² = 2ax

      where v_f, v_i and a are the same as above and x = distance

 

On the earth, a = -32 ft/sec²  (a is negative in this case since it is in the opposite direction of the initial velocity).

 

On the moon, the acceleration due to gravity is 1/6 that of the earth, so a = -32/6 = -5.33 ft/sec²  (again a is negative in this case since it is in the opposite direction of the initial velocity).

 

Now, let's look at the questions for earth:

     1)  To calculate hang time, we need to determine how long it took Jake to reach his highest point (when his final velocity is 0 ft/sec).  The hang time will be twice this time since it will take the same amount of time to return.

 

     v_f - v_i = at

     0 - 8 = -32(t) 

     t =  1/4 seconds

   Hang time on earth= 2t = 2(1/4 seconds) = 1/2 seconds

 

     2) To calculate maximum jump height, we use eqn (2) and solve for x:

     v_{f² -} v_i² =2ax

     0 - (8)² = 2(-32)x

     -64 = -64x

     x = 1 foot on earth

 

 

Repeat for the moon:

     1) Hang time:

          v_f - v_i = at

          0 - 8  = -5.33t

          t = 1.5 seconds

         Hang time on moon equals 2t = 2(1.5 seconds) = 3 seconds

 

     2) Maximum Jump Height:

         v_{f² -} v_i² = 2ax

         0 - (8)² = 2(-5.33)x

         -64 = -10.66x

          x = 6 feet on moon

 

As expected, Jake would have a longer hang time and higher jump height on the moon since the gravitational pull is less.

 

Hope this helps!