You are unloading boxes at your afterschool job and need to push them up a 2 m r

Question

You are unloading boxes at your afterschool job and need to push them up a 2 m ramp at an angle of 30 degree. You want to give it one quick shove so that it will exactly reach the top where your co-worker will lift it off the ramp before it begins to fall again. In other words, you give it a short, sharp push so that it has some initial velocity v_i and it will then travel so that after it has traveled exactly 2 m from the end of your push it has a velocity of v = 0. a. What is the acceleration due to gravity along the ramp? b. What is the time it takes for the box to go up the ramp and what initial velocity do you need to give to the box?

Explanation / Answer

Given that

initial velocity vo

distance s=2 m

angle=30 degree

now we find the acceleration due to gravity on ramp

2=uo^2*sin^2(30)/2g

g=16/vo^2

now we find the taken to go up to ramp

time t=[2s/g]^1/2=[2*2/9.8]^1/2=0.64 sec

now we find the initial velocity

u^2sin^2(30)=2*9.8*2

v^2=156.8

speed Vo=12.5 m/s

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