How far does the jumper move horizontally?

Question

A long jumper achieves a height of 1.5 meters when her initial horizontal velocity is 5m/s. How far does the jumper move horizontally? (Hint: She reaches a height of 1.5 meters halfway through the jump.)

Answer 1

The trick is to use the max height to calculate the time required for the full jump.  

 

Imagine the person was dropped from a height of 1.5m.  How long does it take for them to hit the ground?  The answer is the same if the person is moving horizontally.  So if we use the equation d = v_ot +1/2at^2 and set d = 1.5 and v_o to 0 because there is no initial vertical velocity (i.e. velocity in the y direction at the top of the jump)  then we use a = 9.8 (gravity) we solve for t we get 0.55 sec.  But this is only the time it takes to go from the top of the jump to the ground.  We need to double this to get the time of the full jump.  So the full time is 1.106 sec.  Now to get the distance the jumper moved horizontally, or the range, we simply need to multiple the total time (1.106 sec) by the initial velocity (5 m/s).  Velocity x time = distance.  So the answer should be 5.53 meters.

 

Hope this helps.