Question

Estimate by what factor a person can jump farther on the Moon as compared to the Earth if the takeoff speed and angle are the same. The acceleration due to gravity on the Moon is one-sixth what it is on Earth. Express your answer as an integer.

Answer 1

Let's make an assumption that an object are thrown with initial velocity of to and angle of a above the horizontal level. Then horisontal (x) and vertical (1) velocities Cxdirection - paralled to ground level and y- perpendicular to ground level) are: x = Vxo = Vo cos(x) Vy = Vo sin(a) The time, when the object reaches the manimal height (i velocity component equals zero), can be found: Vy = Vg - atup to tup = Vago Thus, total time in the air is two times longer: a t=ckup = [2 vo x sin(x)]

The animal distance is determined due to the equation: x= Vaxt = vo XC92 (@) x [2 x since] x = V x sin (20), which means x proportional to Ya Taking into the acceleration on the moon is of am = 1 ae , a ratio between manimal distances on the moon (xm) and on the earth (Xe) equals: am Answer: The maximal distance on the moon is 6 times longer than on the earth. for the lunched object with the same take all speed and angle.